Journal Articles

WaterLily.jl: A differentiable and backendagnostic Julia solver to simulate incompressible viscous flow and dynamic bodiesWeymouth, G. D., & Font, B. (2024, submitted).Integrating computational fluid dynamics (CFD) software into optimization and machinelearning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible highlevel languages. In this work, we introduce WaterLily.jl: an opensource incompressible viscous flow solver written in the Julia language. An immersed boundary method is used to enforce the effect of solid boundaries on flow past complex geometries with arbitrary motions. The small code base is multidimensional, multiplatform and backendagnostic (serial and multithreaded CPU, and GPU execution). Additionally, the dynamically typed language allows the solver to be fully differentiable using automatic differentiation. The computational time per time step scales linearly with the number of degrees of freedom (DOF) on CPUs, and we measure up to a 200x speedup using CUDA kernels resulting in a cost of 1.44 nanoseconds per DOF and time step. This leads to comparable performance with lowlevel CFD solvers written in C and Fortran on researchscale problems, opening up exciting possible future applications on the cutting edge of machinelearning research.
@article{WeymouthFont2024, author = {Weymouth, G.D. and Font, B.}, year = {2024, submitted}, title = {{WaterLily.jl: A differentiable and backendagnostic Julia solver to simulate incompressible viscous flow and dynamic bodies}}, eprint = {https://arxiv.org/pdf/2407.16032} }

Deep reinforcement learning for active flow control in a turbulent separation bubbleFont, B., AlcántaraÁvila, F., Rabault, J., Vinuesa, R., & Lehmkuhl, O. (2024, submitted).
@article{Font2024b, author = {Font, B. and AlcántaraÁvila, F. and Rabault, J. and Vinuesa, R. and Lehmkuhl, O.}, year = {2024, submitted}, title = {Deep reinforcement learning for active flow control in a turbulent separation bubble}, eprint = {https://www.researchsquare.com/article/rs4565966/v1.pdf?c=1719317674000} }

Active flow control for drag reduction through multiagent reinforcement learning on a turbulent cylinder at Re_D=3900Suárez, P., ÁlcantaraÁvila, F., Rabault, J., Miró, A., Font, B., Lehmkuhl, O., & Vinuesa, R. (2024, submitted).This study presents novel activeflowcontrol (AFC) strategies aimed at achieving drag reduction for a threedimensional cylinder immersed in a flow at a Reynolds number based on freestream velocity and cylinder diameter of (Re_D=3900). The cylinder in this subcritical flow regime has been extensively studied in the literature and is considered a classic case of turbulent flow arising from a bluff body. The strategies presented are explored through the use of deep reinforcement learning. The cylinder is equipped with 10 independent zeronetmassflux jet pairs, distributed on the top and bottom surfaces, which define the AFC setup. The method is based on the coupling between a computationalfluiddynamics solver and a multiagent reinforcementlearning (MARL) framework using the proximalpolicyoptimization algorithm. Thanks to the acceleration in training facilitated by exploiting the local invariants with MARL, a drag reduction of (8%) was achieved, with a mass cost efficiency two orders of magnitude lower than those of the existing classical controls in the literature. This development represents a significant advancement in active flow control, particularly in turbulent regimes critical to industrial applications.
@article{Suarez2024b, eprint = {https://arxiv.org/pdf/2405.17655}, author = {Suárez, P. and ÁlcantaraÁvila, F. and Rabault, J. and Miró, A. and Font, B. and Lehmkuhl, O. and Vinuesa, R.}, title = {Active flow control for drag reduction through multiagent reinforcement learning on a turbulent cylinder at {$Re_D=3900$}}, publisher = {arXiv}, year = {2024, submitted} }

Flow control of threedimensional cylinders transitioning to turbulence via multiagent reinforcement learningSuárez, P., ÁlcantaraÁvila, F., Rabault, J., Miró, A., Font, B., Lehmkuhl, O., & Vinuesa, R. (2024, submitted).Designing activeflowcontrol (AFC) strategies for threedimensional (3D) bluff bodies is a challenging task with critical industrial implications. In this study we explore the potential of discovering novel control strategies for drag reduction using deep reinforcement learning. We introduce a highdimensional AFC setup on a 3D cylinder, considering Reynolds numbers (Re_D) from 100 to 400, which is a range including the transition to 3D wake instabilities. The setup involves multiple zeronetmassflux jets positioned on the top and bottom surfaces, aligned into two slots. The method relies on coupling the computationalfluiddynamics solver with a multiagent reinforcementlearning (MARL) framework based on the proximalpolicyoptimization algorithm. MARL offers several advantages: it exploits local invariance, adaptable control across geometries, facilitates transfer learning and crossapplication of agents, and results in a significant training speedup. For instance, our results demonstrate 21% drag reduction for Re_D=300, outperforming classical periodic control, which yields up to 6% reduction. To the authors’ knowledge, the present MARLbased framework represents the first time where training is conducted in 3D cylinders. This breakthrough paves the way for conducting AFC on progressively more complex turbulentflow configurations.
@article{Suarez2024a, author = {Suárez, P. and ÁlcantaraÁvila, F. and Rabault, J. and Miró, A. and Font, B. and Lehmkuhl, O. and Vinuesa, R.}, title = {Flow control of threedimensional cylinders transitioning to turbulence via multiagent reinforcement learning}, eprint = {https://arxiv.org/pdf/2405.17655}, publisher = {arXiv}, year = {2024, submitted} }

Hydrothermal liquefaction of Spanish crude olive pomace for biofuel and biochar productionCutz, L., Misara, S., Font, B., AlNaji, M., & de Jong, W. (2024, submitted).
@article{Cutz2024, author = {Cutz, L. and Misara, S. and Font, B. and AlNaji, M. and de Jong, W.}, year = {2024, submitted}, title = {Hydrothermal liquefaction of Spanish crude olive pomace for biofuel and biochar production} }

A datadriven nonequilibrium wall model for LES of transitional flowsRadhakrishnan, S., Calafell, J., Miró, A., Font, B., & Lehmkuhl, O. (2024). International Journal of Numerical Methods for Heat & Fluid Flow.
@article{Radhakrishnan2024, author = {Radhakrishnan, S. and Calafell, J. and Mir\'{o}, A. and Font, B. and Lehmkuhl, O.}, year = {2024}, title = {A datadriven nonequilibrium wall model for {LES} of transitional flows}, doi = {10.1108/HFF1120230710}, journal = {International Journal of Numerical Methods for Heat \& Fluid Flow}, eprint = {https://www.emerald.com/insight/content/doi/10.1108/HFF1120230710/full/pdf?title=datadrivenwallmodelingforlesinvolvingnonequilibriumboundarylayereffects} }

Deep reinforcement learning for flow control exploits different physics for increasing Reynolds number regimesVarela, P., Suárez, P., AlcántaraÁvila, F., Miró, A., Rabault, J., Font, B., GarcíaCuevas, L. M., Lehmkuhl, O., & Vinuesa, R. (2022). Actuators, 11(12).The increase in emissions associated with aviation requires deeper research into novel sensing and flowcontrol strategies to obtain improved aerodynamic performances. In this context, datadriven methods are suitable for exploring new approaches to control the flow and develop more efficient strategies. Deep artificial neural networks (ANNs) used together with reinforcement learning, i.e., deep reinforcement learning (DRL), are receiving more attention due to their capabilities of controlling complex problems in multiple areas. In particular, these techniques have been recently used to solve problems related to flow control. In this work, an ANN trained through a DRL agent, coupled with the numerical solver Alya, is used to perform active flow control. The Tensorforce library was used to apply DRL to the simulated flow. Twodimensional simulations of the flow around a cylinder were conducted and an active control based on two jets located on the walls of the cylinder was considered. By gathering information from the flow surrounding the cylinder, the ANN agent is able to learn through proximal policy optimization (PPO) effective control strategies for the jets, leading to a significant drag reduction. Furthermore, the agent needs to account for the coupled effects of the friction and pressuredrag components, as well as the interaction between the two boundary layers on both sides of the cylinder and the wake. In the present work, a Reynolds number range beyond those previously considered was studied and compared with results obtained using classical flowcontrol methods. Significantly different forms of nature in the control strategies were identified by the DRL as the Reynolds number Re increased. On the one hand, for Re<1000, the classical control strategy based on an opposition control relative to the wake oscillation was obtained. On the other hand, for Re=2000, the new strategy consisted of energization of the boundary layers and the separation area, which modulated the flow separation and reduced the drag in a fashion similar to that of the drag crisis, through a highfrequency actuation. A crossapplication of agents was performed for a flow at Re=2000, obtaining similar results in terms of the drag reduction with the agents trained at Re=1000 and 2000. The fact that two different strategies yielded the same performance made us question whether this Reynolds number regime (Re=2000) belongs to a transition towards a naturedifferent flow, which would only admits a highfrequency actuation strategy to obtain the drag reduction. At the same time, this finding allows for the application of ANNs trained at lower Reynolds numbers, but are comparable in nature, saving computational resources.
@article{Varela2022, author = {Varela, P. and Suárez, P. and AlcántaraÁvila, F. and Mir\'{o}, A. and Rabault, J. and Font, B. and GarcíaCuevas, L.M. and Lehmkuhl, O. and Vinuesa, R.}, year = {2022}, title = {Deep reinforcement learning for flow control exploits different physics for increasing Reynolds number regimes}, journal = {Actuators}, volume = {11}, number = {12}, articlenumber = {359}, doi = {10.3390/act11120359}, eprint = {https://www.mdpi.com/20760825/11/12/359/pdf?version=1669977565} }

Deep learning of the spanwiseaveraged Navier–Stokes equationsFont, B., Weymouth, G. D., Nguyen, V.T., & Tutty, O. R. (2021). Journal of Computational Physics, 434, 110199.Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as striptheory and depthaveraged methods do not take into account the natural flow dissipation mechanism inherent in the smallscale threedimensional (3D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwiseaveraged Navier–Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3D effects otherwise not considered in 2D formulations. A supervised machinelearning (ML) model based on a deep convolutional neural network provides closure to the SANS system. Apriori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shearlayer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for aposteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 110%. This results in approximately an order of magnitude improvement over standard 2D simulations while reducing the computational cost of 3D simulations by 99.5%.
@article{Font2021, author = {Font, B. and Weymouth, G.D. and Nguyen, V.T. and Tutty, O.R.}, year = {2021}, title = {Deep learning of the spanwiseaveraged {N}avier{S}tokes equations}, journal = {Journal of Computational Physics}, volume = {434}, pages = {110199}, issn = {00219991}, doi = {10.1016/j.jcp.2021.110199}, eprint = {https://arxiv.org/pdf/2008.07528} }

Span effect on the turbulence nature of flow past a circular cylinderFont, B., Weymouth, G. D., Nguyen, V.T., & Tutty, O. R. (2019). Journal of Fluid Mechanics, 878, 306–323.Turbulent flow evolution and energy cascades are significantly different in twodimensional (2D) and threedimensional (3D) flows. Studies have investigated these differences in obstaclefree turbulent flows, but solid boundaries have an important impact on the crossover between 3D to 2D turbulence dynamics. In this work, we investigate the span effect on the turbulence nature of flow past a circular cylinder at Re=10^4. It is found that even for highly anisotropic geometries, 3D smallscale structures detach from the walls. Additionally, the natural largescale rotation of the Kármán vortices rapidly twodimensionalises those structures if the span is 50% of the diameter or less. We show this is linked to the span being shorter than the Mode B instability wavelength. The conflicting 3D smallscale structures and 2D Kármán vortices result in 2D and 3D turbulence dynamics which can coexist at certain locations of the wake depending on the domain geometric anisotropy.
@article{Font2019, doi = {10.1017/jfm.2019.637}, year = {2019}, publisher = {Cambridge University Press ({CUP})}, volume = {878}, pages = {306323}, author = {Font, B. and Weymouth, G.D. and Nguyen, V.T. and Tutty, O.R.}, title = {Span effect on the turbulence nature of flow past a circular cylinder}, journal = {Journal of Fluid Mechanics}, eprint = {https://arxiv.org/pdf/2008.08933} }
Peerreviewed Symposium Proceedings

Active flow control of a turbulent separation bubble through deep reinforcement learningFont, B., AlcántaraÁvila, F., Rabault, J., Vinuesa, R., & Lehmkuhl, O. (2024). Journal of Physics: Conference Series, 2753(1), 012022.The control efficacy of classical periodic forcing and deep reinforcement learning (DRL) is assessed for a turbulent separation bubble (TSB) at Re_τ=180 on the upstream region before separation occurs. The TSB can resemble a separation phenomenon naturally arising in wings, and a successful reduction of the TSB can have practical implications in the reduction of the aviation carbon footprint. We find that the classical zeronetmasflux (ZNMF) periodic control is able to reduce the TSB by 15.7%. On the other hand, the DRLbased control achieves 25.3% reduction and provides a smoother control strategy while also being ZNMF. To the best of our knowledge, the current test case is the highest Reynoldsnumber flow that has been successfully controlled using DRL to this date. In future work, these results will be scaled to wellresolved largeeddy simulation grids. Furthermore, we provide details of our opensource CFD–DRL framework suited for the next generation of exascale computing machines.
@inproceedings{Font2024a, author = {Font, B. and AlcántaraÁvila, F. and Rabault, J. and Vinuesa, R. and Lehmkuhl, O.}, year = {2024}, publisher = {IOP Publishing}, title = {Active flow control of a turbulent separation bubble through deep reinforcement learning}, journal = {Journal of Physics: Conference Series}, volume = {2753}, number = {1}, pages = {012022}, doi = {10.1088/17426596/2753/1/012022}, eprint = {https://arxiv.org/pdf/2403.20295} }

A datadriven wallshear stress model for LES using gradient boosted decision treesRadhakrishnan, S., Gyamfi, L. A., Miró, A., Font, B., Calafell, J., & Lehmkuhl, O. (2021). ISC High Performance Computing Conference, 105–121.With the recent advances in machine learning, datadriven strategies could augment wall modeling in large eddy simulation (LES). In this work, a wall model based on gradient boosted decision trees is presented. The model is trained to learn the boundary layer of a turbulent channel flow so that it can be used to make predictions for significantly different flows where the equilibrium assumptions are valid. The methodology of building the model is presented in detail. The experiment conducted to choose the data for training is described. The trained model is tested a posteriori on a turbulent channel flow and the flow over a wallmounted hump. The results from the tests are compared with that of an algebraic equilibrium wall model, and the performance is evaluated. The results show that the model has succeeded in learning the boundary layer, proving the effectiveness of our methodology of datadriven model development, which is extendable to complex flows.
@inproceedings{Radhakrishnan2021, author = {Radhakrishnan, S. and Gyamfi, L.A. and Mir\'{o}, A. and Font, B. and Calafell, J. and Lehmkuhl, O.}, year = {2021}, title = {A datadriven wallshear stress model for LES using gradient boosted decision trees}, booktitle = {ISC High Performance Computing Conference}, publisher = {Springer International Publishing}, pages = {105121}, isbn = {9783030905392}, doi = {10.1007/9783030905392_7}, eprint = {https://upcommons.upc.edu/bitstream/handle/2117/358666/Contribution_TitleSupported_by_organization_x___2_.pdf?sequence=6&isAllowed=y} }

Turbulent wake prediction using deep convolutional neural networksFont, B., Weymouth, G. D., Nguyen, V.T., & Tutty, O. R. (2020). 33rd Symposium on Naval Hydrodynamics.A machinelearning based closure is explored for the prediction of the turbulent wake of flow past a circular cylinder at a high Reynolds number. We show that classic turbulence closures based on the turbulentviscosity hypothesis are not capable of modelling the nonlinear relationship between the mean quantities and the target turbulent fields. Instead, different multipleinput multipleoutput autoencoder convolutional neural networks are explored in this work to develop a datadriven closure. A detailed hyperparameter study is completed including network architecture, loss functions and input sets, among others. Apriori results show 80% to 90% correlation coefficients between target and predicted turbulent fields of previously unseen data. High correlation coefficients are rapidly achieved by networks with a large number of trainable parameters, whereas smaller networks require more training epochs. The integration of the model in live simulations is theoretically discussed from its stability standpoint as well as preliminary physicsbased constraints ideas to provide more stable datadriven closures.
@inproceedings{Font2020a, year = {2020}, author = {Font, B. and Weymouth, G.D. and Nguyen, V.T. and Tutty, O.R.}, title = {Turbulent wake prediction using deep convolutional neural networks}, booktitle = {33rd Symposium on Naval Hydrodynamics}, organization = {Office of Naval Research, US}, eprint = {https://bfg.github.io/assets/pdf/Font_et_al_2020_Turbulent_wake_prediction_using_deep_convolutional_neural_networks.pdf} }
Conference Proceedings

WaterLily.jl: A differentiable fluid simulator in Julia with fast heterogeneous executionWeymouth, G. D., & Font, B. (2023). In ParCFD 2023, Cuenca (Ecuador).Integrating computational fluid dynamics (CFD) software into optimization and machinelearning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible highlevel languages. WaterLily.jl is an opensource incompressible viscous flow solver written in the Julia language. The small code base is multidimensional, multiplatform and backendagnostic (serial CPU, multithreaded, & GPU execution). The simulator is differentiable and uses automaticdifferentiation internally to immerse solid geometries and optimize the pressure solver. The computational time per time step scales linearly with the number of degrees of freedom on CPUs, and we see up to a 182x speedup using CUDA kernels. This leads to comparable performance with Fortran solvers on many researchscale problems opening up exciting possible future applications on the cutting edge of machinelearning research.
@proceedings{Weymouth2023ParCFD, author = {Weymouth, G.D. and Font, B.}, title = {Water{L}ily.jl: A differentiable fluid simulator in {J}ulia with fast heterogeneous execution}, year = {2023}, booktitle = {ParCFD 2023, Cuenca (Ecuador)}, eprint = {https://arxiv.org/pdf/2304.08159} }

Active flow control for threedimensional cylinders through deep reinforcement learningSuárez, P., AlcántaraÁvila, F., Miró, A., Rabault, J., Font, B., Lehmkuhl, O., & Vinuesa, R. (2023). In 14th International ERCOFTAC Symposium on Engineering, Turbulence, Modelling and Measurements.This paper presents for the first time successful results of active flow control with multiple independently controlled zeronetmassflux synthetic jets. The jets are placed on a threedimensional cylinder along its span with the aim of reducing the drag coefficient. The method is based on a deepreinforcementlearning framework that couples a computationalfluiddynamics solver with an agent using the proximalpolicyoptimization algorithm. We implement a multiagent reinforcement learning framework which offers numerous advantages: it exploits local invariants, makes the control adaptable to different geometries, facilitates transfer learning and crossapplication of agents and results in significant training speedup. In this contribution we report significant drag reduction after applying the DRLbased control in three different configurations of the problem.
@proceedings{Suarez2023a, author = {Suárez, P. and AlcántaraÁvila, F. and Mir\'{o}, A. and Rabault, J. and Font, B. and Lehmkuhl, O. and Vinuesa, R.}, title = {Active flow control for threedimensional cylinders through deep reinforcement learning}, year = {2023}, booktitle = {14th International ERCOFTAC Symposium on Engineering, Turbulence, Modelling and Measurements}, eprint = {https://arxiv.org/pdf/2309.02462} }

Analysis of twodimensional and threedimensional wakes of long circular cylindersFont, B., Weymouth, G. D., & Tutty, O. R. (2017). In OCEANS 2017. IEEE.The wake behind a bluff body constitutes an intrinsically threedimensional flow and it is known that twodimensional simulations yield to an unphysical prediction of the body forces because of the nature of the twodimensional NavierStokes equations. However, threedimensional simulations are too computationally expensive for cases such as marine risers, which have very large aspect ratios and are exposed to a high Reynolds number flow. A quantitative and qualitative study has been performed to investigate the fundamental differences on the wake of twodimensional and threedimensional fixed spanwise periodic cylinders for a Reynolds number of 10^4. A very fine unifrom grid (503M points) has been used for the near and mid wake range, and it is shown that the wake presents very different vortical structures when the spanwise dimensionality is omitted. In this case, forces such as lift and drag are overpredicted. The kinetic energy spectra of the flow is also investigated to further discuss the physics inherent of each case together and it is found that the contribution of the spanwise velocity on the large wavenumbers is significantly smaller than the other velocity components.
@proceedings{Font2017, doi = {10.1109/oceanse.2017.8084904}, year = {2017}, publisher = {{IEEE}}, author = {Font, B. and Weymouth, G.D. and Tutty, O.R.}, title = {Analysis of twodimensional and threedimensional wakes of long circular cylinders}, booktitle = {{OCEANS} 2017}, eprint = {https://eprints.soton.ac.uk/411819/1/Font_Garcia_et_al_2017_Analysis_of_two_dimensional_and_three_dimensional_wakes_of_long_circular_cylinders.pdf} }
Conference Abstracts

WaterLily.jl: A fast and flexible CFD solver with heterogeneous executionFont, B., & Weymouth, G. D. (2024). JuliaCon 2024, Eindhoven (Netherlands).In this talk, we will review how [WaterLily.jl](https://github.com/weymouth/WaterLily.jl), a computational fluid dynamics Julia solver, has been ported from its original serialCPU implementation to a backendagnostic solver that can be seamlessly executed using multithreading in CPUs or in GPUs of different vendors. The transition has been accomplished using a metaprogramming approach that generalizes the implementation of array iterators while also relying on [KernelAbstractions.jl](https://github.com/JuliaGPU/KernelAbstractions.jl) to specialize each kernel on the target architecture. In singleGPU tests, we show that [WaterLily.jl](https://github.com/weymouth/WaterLily.jl) is as fast as stateoftheart CFD solvers written C++ or Fortran. Finally, we also discuss the potential of integrating ML models and differentiability into the solver.
@conference{Font2024JuliaCon, author = {Font, B. and Weymouth, G.D.}, title = {{WaterLily.jl: A fast and flexible CFD solver with heterogeneous execution}}, year = {2024}, booktitle = {JuliaCon 2024, Eindhoven (Netherlands)}, url = {https://juliacon.org/2024/minisymposia/hpc/} }

Turbulent separation bubble control using deep reinforcement learning in preexascale machinesFont, B., AlcántaraÁvila, F., Rabault, J., Vinuesa, R., & Lehmkuhl, O. (2024). ECCOMAS Congress 2024, Lisbon (Portugal).Deep reinforcement learning (DRL) for active flow control (AFC) has recently emerged as a promising alternative to classical control based on fluiddynamics theory (Vignon et al. 2023). The everincreasing computing power is closing the gap of incorporating scaleresolving fluid dynamics simulations into the DRL trialanderror training loop. In this direction, we investigate the control efficacy of DRL in reducing a turbulent separation bubble (TSB) generated by and adversepressure gradient turbulent boundary layer. TSB is a naturally arising phenomenon in aircraft wings operating at high angles of attack, and an adequate control could yield safer maneuvers and a reduced fuel consumption. We find that the DRL agent is able to learn a successful control strategy eventually yielding a larger TSB reduction than classical periodic forcing control. Moreover, we assess the potential of transfer learning by comparing results from a DRL agent trained in both a coarse largeeddy simulation (LES) and a fine wellresolved LES. Finally, we introduce our opensource framework composed by the multiGPU CFD solver SOD2D (Gasparino et al. 2023) and the DRL model implemented in SmartSOD2D, which also handles the communication between CFD solver and DRL agent using SmartSim (Partee et al. 2022). The natural nested parallelism of the training strategy, which consist in using multiple parallel CFD simulations feeding data into a single DRL agent, allows to properly harvest the computing power of preexascale machines.
@conference{Font2024ECCOMAS, author = {Font, B. and AlcántaraÁvila, F. and Rabault, J. and Vinuesa, R. and Lehmkuhl, O.}, title = {Turbulent separation bubble control using deep reinforcement learning in preexascale machines}, year = {2024}, booktitle = {{ECCOMAS} {C}ongress 2024, Lisbon (Portugal)}, url = {https://eccomas2024.org/event/contribution/df2a8b4695f011ee8178000c29ddfc0c} }

Towards active flow control strategies through deep reinforcement learningMontalà, R., Font, B., Lehmkuhl, O., Vinuesa, R., & Rodriguez, I. (2024). ECCOMAS Congress 2024, Lisbon (Portugal).The present work proposes to explore deep reinforcement learning (DRL) methods for designing optimal active flow control (AFC) strategies for drag reduction using synthetic jets in wings. In the present study, the SD7003 airfoil is investigated at Re=60,000 and considering two angles of attack, 4^∘ and 14^∘. Therefore, the capabilities of combining DRL and AFC in reducing the drag coefficient in wings is assessed for both, wallbounded and massive separated conditions, respectively.
@conference{Montala2024ECCOMAS, author = {Montalà, R. and Font, B. and Lehmkuhl, O. and Vinuesa, R. and Rodriguez, I.}, title = {Towards active flow control strategies through deep reinforcement learning}, year = {2024}, booktitle = {{ECCOMAS} {C}ongress 2024, Lisbon (Portugal)}, url = {https://eccomas2024.org/event/contribution/735ccf31b3cd11eeac5b000c29ddfc0c} }

φ–flow: A novel physicsconstrained architecture to enforce incompressibility and boundary conditions for fast and accurate flow predictionsCabral, M., Font, B., & Weymouth, G. D. (2024). ECCOMAS Congress 2024, Lisbon (Portugal).Deep learning models have demonstrated remarkable capabilities at producing fast predictions of complex flow fields. However, incorporating known physics is essential to ensure that physical solutions can generalize to flow regimes not used for training. In this work, a novel architecture that (by construction) enforces both flow incompressibility and nopenetration boundary conditions is introduced. The method is a hybrid approach, combining recent deep learning techniques with more classical computational fluid dynamics methodologies. Differently from the softconstraints variants, a hardconstraints architecture can enforce physical conditions not only during training but at inference too. Furthermore, our model is more data efficient and allows for significantly smaller neural networks, being more suitable for real world problems where data and computational resources are often limited. The new φ–flow model is compared with the wellknown physicsinformed neural net work (PINN) model, and a baseline (no physics) NN model. Canonical test cases as well as a more challenging airfoil problem are considered. The robustness of the model is an important contribution to the stateoftheart of scientific machine learning for flow predictions, which can target a wide range of applications, from superresolution to topological optimization.
@conference{Cabral2024ECCOMAS, author = {Cabral, M. and Font, B. and Weymouth, G.D.}, title = {$\phi$flow: {A} novel physicsconstrained architecture to enforce incompressibility and boundary conditions for fast and accurate flow predictions}, year = {2024}, booktitle = {{ECCOMAS} {C}ongress 2024, Lisbon (Portugal)}, url = {https://eccomas2024.org/event/contribution/6c698867969b11ee8a2d000c29ddfc0c} }

The effect of physical constraints on the loss function landscapes of deep learningCabral, M., Font, B., & Weymouth, G. D. (2023). 76th APS Division of Fluid Dynamics Meeting Abstracts, Washington DC (US).Deep learning models have demonstrated remarkable capabilities at producing fast predictions of complex flow fields. However, incorporating known physics is essential to ensure physically consistent solutions generalize to outofsample data. This research investigates the impact of different approaches to impose flow incompressibility and nopenetration boundary conditions on deep learning flow field predictions. This study finds that hard constraints lead to a notably more complex loss landscape, making it more difficult to fit a lowerror model. This is compared to the lossfunction landscape resulting from a soft constraints approach, where the data lossfunction is augmented with additional field and boundary terms, such as in physicsinformed neural networks. Finally, the importance of these constraint strategies is studied during extrapolation and prediction of physical quantities, such as lift and drag in an airfoil. This work’s findings shed light on the challenges and tradeoffs involved in incorporating physics into deep learning models, offering valuable insights for future research in physicsinformed machine learning.
@conference{Cabral2023APS, author = {Cabral, M. and Font, B. and Weymouth, G.D.}, title = {The effect of physical constraints on the loss function landscapes of deep learning}, year = {2023}, booktitle = {76th APS Division of Fluid Dynamics Meeting Abstracts, Washington DC (US)}, url = {https://meetings.aps.org/Meeting/DFD23/Session/L29.1} }

Deep reinforcement learning for active separation control in a turbulent boundary layerAlcántaraÁvila, F., Font, B., Rabault, J., Vinuesa, R., & Lehmkuhl, O. (2023). 76th APS Division of Fluid Dynamics Meeting Abstracts, Washington DC (US).Active flow control to reduce the bubble of recirculation (BR) in a separated turbulent boundary layer is investigated using deep reinforcement learning (DRL). The BR is induced by imposing a wallnormal blowing and suction at the top of the domain, which generates the separation. The separation control is performed by several control surfaces in the form of rectangular jets placed upstream of the BR, alongside the streamwise direction and parallel one to each other in the spanwise direction. These jets apply a wallnormal velocity magnitude defined by the DRL agent. The actions proposed by the DRL agent are based on a partial observation of velocity components at the BR and aim to maximize the accumulated reward in time. In this case, the wall shear stress is used as a reward proxy of the BR length. Since the flow is periodic in the spanwise direction, the domain can be divided into invariant subdomains that allows us to use the multiagent reinforcement learning technique. This technique exploits the invariants of the domain to generate multiple explorations within a single large eddy simulation. Comparison with classical control techniques to reduce the BR size is also reported, highlighting the improvements that DRL brings to this case.
@conference{AlcantaraAvila2023APS, author = {AlcántaraÁvila, F. and Font, B. and Rabault, J. and Vinuesa, R. and Lehmkuhl, O.}, title = {Deep reinforcement learning for active separation control in a turbulent boundary layer}, year = {2023}, booktitle = {76th APS Division of Fluid Dynamics Meeting Abstracts, Washington DC (US)}, url = {https://meetings.aps.org/Meeting/DFD23/Session/A30.8} }

WaterLily: A fast differentiable CPU/GPU flow simulator in JuliaWeymouth, G. D., & Font, B. (2023). 76th APS Division of Fluid Dynamics Meeting Abstracts, Washington DC (US).Integrating computational fluid dynamics CFD software into optimization and machinelearning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible highlevel languages. WaterLily is an opensource incompressible viscous flow solver written in the Julia language. The small code base is multidimensional, multiplatform and backendagnostic (serial CPU, multithreaded, & GPU execution). The simulator is differentiable and uses automaticdifferentiation internally to immerse solid geometries and optimize the pressure solver. The computational time per time step scales linearly with the number of degrees of freedom on CPUs, and we see up to a 182x speedup using CUDA kernels. This leads to comparable performance with Fortran solvers on many researchscale problems opening up exciting possible future applications on the cutting edge of fluid mechanics and machinelearning research.
@conference{Weymouth2023APS, author = {Weymouth, G.D. and Font, B.}, title = {Water{L}ily: {A} fast differentiable {CPU/GPU} flow simulator in {J}ulia}, year = {2023}, booktitle = {76th APS Division of Fluid Dynamics Meeting Abstracts, Washington DC (US)}, url = {https://meetings.aps.org/Meeting/DFD23/Session/R05.8} }

Separation control in adversepressuregradient turbulent boundary layersAlcántaraÁvila, F., Sanchis, M., Gasparino, L., Muela, J., Font, B., Rabault, J., Lehmkuhl, O., & Vinuesa, R. (2023). European Turbulence Conference 18th, Valencia (Spain).The need to save energy is becoming crucial with the global energy crisis of the past years. The use of flowcontrol techniques has been prevalent in addressing aeronautical problems. These techniques are employed to decrease energy consumption by means of reducing drag forces or optimizing the geometry. In parallel, over the past few decades, the rise in computational power has facilitated the utilization of numerical simulation as a way to investigate wallbounded turbulence. Additionally, as a result of the increased availability of computational resources, there has been an increasing number of investigations in the field of fluid mechanics that involve the implementation of machinelearning techniques over the past decade. By combining these two approaches, we apply active flow control (AFC) to a turbulent boundary layer (TBL) subjected to an adverse pressure gradient (APG) strong enough to produce flow separation. Our approach uses the numerical code Sod, which was developed at the Barcelona Super Computing Center for scaleresolving simulations of compressible fluid flows in aeronautical applications. Sod is based on the spectralelement method (SEM) and offers high performance on generalpurpose graphicalprocessing units (GPUs) and high accuracy by the SEM scheme. To perform the AFC, we use several actuators or jets strategically placed in the domain, which will perform blowing or suction. We connect a neural network to the jets and use the deepreinforcementlearning (DRL) to obtain an effective control strategy. With DRL techniques, the DRL algorithm learns nonlinear control strategies through direct trialanderror. After a sufficient number of episodes, the algorithm can optimize a desired reward function, such as delaying separation in our APG TBL. As part of this study, a parametric analysis of the Clauser–Rotta pressuregradient parameter (β) is performed, where βis defined as β= δ*/τ(dp/dx). Here δ* is the displacement thickness, τis the wallshear stress and dp/dx is the streamwise pressure gradient. Different simulations are performed for each β, which has an almost constant value throughout the entire boundary layer. Moderate to high Reynolds numbers are computed, reaching up to approximately Re_θ= 6000, where Re_θis the Reynolds number based on momentum thickness. A comparison of the different separationcontrol strategies for values of βover ≳7 leading to separation is also presented. The physics of the obtained control strategies are thoroughly detailed.
@conference{AlcantaraAvila2023ETC, author = {AlcántaraÁvila, F. and Sanchis, M. and Gasparino, L. and Muela, J. and Font, B. and Rabault, J. and Lehmkuhl, O. and Vinuesa, R.}, title = {Separation control in adversepressuregradient turbulent boundary layers}, year = {2023}, booktitle = {European Turbulence Conference 18th, Valencia (Spain)} }

Active flow control on threedimensional cylinders through deep reinforcement learningSuárez, P., AlcántaraÁvila, F., Miró, A., Rabault, J., Font, B., Lehmkuhl, O., & Vinuesa, R. (2023). First International Conference Math 2 Product, Taormina (Italy).Deep neural networks (DNNs) used with reinforcement learning (RL), also called deep reinforcement learning (DRL), are used to explore and manage complex systems in a wide range of areas [2]. In this work, a NN trained through a DRL agent, coupled with the numerical solver Alya, is used to perform active flow control (AFC) in a cylinder. Alya, developed in the Barcelona Super Computing Center (BSC), is a parallel solver for partial differential equations using the finiteelement method. It is designed to be used in supercomputers for scaleresolving simulations (both LES and DNS). The Tensorforce library, built on top of Tensorflow, is used to apply DRL to the simulation. DRL techniques consist of a trialanderror sequence, where these sequences are known as episodes. This agent is trained from multiple flowdomain observations and receives a reward function. After a certain number of independent episodes (finite trajectories), the policy is updated based on the reward, so we benefit from this system of batches with the multienvironment approach [4]. The AFC is performed by several actuators or jets, strategically placed on the cylinder surface, which perform either blowing or suction, thus modifying the flow around the cylinder. The agent sends the signal to change actuator mass flow rate throughout many sequenced actions in time. The goal of this work is to apply our knowledge to threedimensional cylinders, with AFC placed in the top and bottom of its surface, reproducing the state of the art at low Reynolds number for twodimensional (2D) cases [3, 4, 5]. As the laminar regime is present in a very lowReynoldsnumber range between 50 and 150, the flow physics and DRLbased control are very similar to those reported for the widelystudied case at Re = 100, with a drag reduction of 8%. The novelty comes as the Reynolds number gradually increases, and thus the structures in the spanwise direction develop. These have an effect on the aerodynamic performance and therefore active flow control has the opportunity to explore and exploit new capabilities. This is where we observe discrepancies with respect to the behavior in 2D. As opposed to what has been previously reported in the literature, in this case we will not consider walls on the top and bottom boundaries of the domain. There is the opportunity to implement new jet configurations, having multiple independent jets along the cylinder. This means having more variables to control, a fact that adds to the challenge of optimising the DRL framework with new tools such as multiagent reinforcement learning (MARL) [1]. We have already reported promising results at a Reynolds number of Re = 2000 in a 2D cylinder, see figure 1, extending previous work [3, 4, 5, 7]. The impact of the control on the wake has been reported, increasing the recirculation bubble and reducing the drag by 8% at Re = 100 and approximately 17% for Re = 2000. At higher Reynolds numbers, the agent attempts to delay the detachment point in the cylinder surface using a highfrequency signal in the actuation of the jets, similar to what can be observed in the dragcrisis phenomenon, see figure 2. This strategy contrasts with the one obtained at a lower Reynolds number, where the agent acts at a lower frequency to perform opposition control. The final conference contribution will include the results in threedimensional cylinders.
@conference{Suarez2023M2P, author = {Suárez, P. and AlcántaraÁvila, F. and Mir\'{o}, A. and Rabault, J. and Font, B. and Lehmkuhl, O. and Vinuesa, R.}, title = {Active flow control on threedimensional cylinders through deep reinforcement learning}, year = {2023}, booktitle = {First International Conference Math 2 Product, Taormina (Italy)} }

On the entropyviscosity method for flux reconstructionFont, B., Miró, A., & Lehmkuhl, O. (2023). 2nd Spanish Fluid Mechanics Conference, Barcelona (Spain).Recent advances in modern computer architectures for highperformance computing (HPC) are paving the path towards a wider adoption of highorder (HO) methods within the computational fluid dynamics (CFD) community. Compared to traditional loworder methods, HO methods promise to achieve an arbitrary level of accuracy at a reduced computational cost, making highfidelity scaleresolving simulations for highspeed flows a reality. Under the highorder methods umbrella, the flux reconstruction (FR) method originally proposed by has been gaining attention due to its simple formulation and unifying framework. It has been shown that FR can recover both nodal DG and SD schemes for linear and spatiallyvarying fluxes, hence the unifying character. During the last decade, research on HO methods for CFD has been focused on achieving a similar level of maturity as traditional loworder methods. With this purpose, we investigate the entropyviscosity shockcapturing scheme by Guermond (2011) for the FR method. The entropyviscosity method forces an entropybased numerical dissipation via effective viscosity near physical discontinuities while vanishing on smooth regions. This helps stabilising the naturally arising oscillations that spectral (HO) methods trigger near discontinuities because of the Gibbs phenomenon. A 1D flux reconstruction solver has been implemented using Julia. The 1D Burgers equation is used with different initial conditions. GaussLegendre and GaussLobbattoLegendre solution points are considered. In contrast to other works, the implementation of the entropyviscosity scheme is performed elementwise, ie. a single elemental viscosity is used taken as the maximum absolute norm of the values computed at the element solution points. This has proven to be more stable than the pointwise counterpart.
@conference{Font2023SFMC, author = {Font, B. and Mir\'{o}, A. and Lehmkuhl, O.}, title = {On the entropyviscosity method for flux reconstruction}, year = {2023}, booktitle = {2nd Spanish Fluid Mechanics Conference, Barcelona (Spain)}, eprint = {https://bfg.github.io/assets/pdf/Font_et_al_2023_On_the_entropy_viscosity_method_for_flux_reconstruction.pdf} }

Progress in highorder largeeddy simulation of aeronautical flows using the integrallength scale approximation turbulence modelFont, B., Naddei, F., & Lehmkuhl, O. (2022). 3rd HighFidelity Industrial LES/DNS Symposium, Brussels (Belgium).Highorder discretization methods for computational fluid dynamics have become more popular in the recent years due to the increasing computational capacity of highperformance computing facilities. Current efforts in the highorder method community are dedicated to achieve the same level of robustness and maturity as traditional loworder finitevolume and finitedifference methods. In this scenario, the use of stateoftheart turbulence models for highorder largeeddy simulation (LES) remains an open front. In this work, we investigate the performance of the integrallength scale approximation (ILSA) turbulence model on a discontinuousGalerkin spectralelement method (DGSEM) solver. Additionally, the finitevolume version of the solver is also considered for comparison purposes. Differently from other turbulence models, ILSA bases the filter width on the flow turbulence properties instead of the grid size thus making it suitable for h/padapting highorder methods as well as highly anisotropic grids. The ILSA model is first validated on a turbulent channel flow at Re_τ=950 using a wallmodelled grid, where an equilibrium wall model is employed near the solid boundaries. While setting the wall model exchange location at y^+=15 yields the wellknown loglayer mismatch, accurate results are obtained when the wall model exchange location is moved away from the wall at y^+=100. On both discretization strategies, ILSA yields improved turbulence statistics compared to an implicit turbulence modelling approach (\textitaka. implicit LES or iLES). Both ILSA and iLES modelling strategies are further assessed on the jet exhaust aerodynamics and noise (JEAN) test case. This case aims to simulate the aerodynamics of a typical commercial aircraft jet engine exhaust in cruise conditions and it also provides an estimation of the noise generated by the exhausting jet. Two different meshes are used – a highly anisotropic linear mesh and a finer quadratic mesh. Results for mean and fluctuating velocity profiles are presented on both meshes. It is shown that ILSA outperforms the iLES approach compared to experimental data at an increased computation cost. The iLES simulation is also used for an acoustic analysis based on the Ffowcs Williams–Hawkings acoustic analogy. It is found that the quadratic mesh improves the results of the linear mesh on the highfrequency region. In summary, the use of the ILSA turbulence model is demonstrated on a highorder solver for a LES of an aeronautical flow, extending the work of Lehmkuhl 2019. Future investigations are set on testing other aeronautical flows such as the common research model (CRM) in highlift configuration.
@conference{Font2022HiFiLED, author = {Font, B. and Naddei, F. and Lehmkuhl, O.}, title = {Progress in highorder largeeddy simulation of aeronautical flows using the integrallength scale approximation turbulence model}, year = {2022}, booktitle = {3rd HighFidelity Industrial LES/DNS Symposium, Brussels (Belgium)} }

Turbulence models assessment using finitevolume and highorder methods for aeronautical applicationsFont, B., Naddei, F., & Lehmkuhl, O. (2022). ECCOMAS Congress 2022, Oslo (Norway).With the imminent advance of highperformance computing for exascale architectures, the use of highorder methods for scaleresolving aeronautical simulations is becoming a reality. In this new framework, there is the need to reassess longused turbulence closures and wall models, which have been traditionally tested in loworder methods. To this end, the LES WALE and Vreman models are selected and implemented using finitevolume and discontinuousGalerkin (DG) discretizations, thus allowing a direct comparison of their convergence properties on different schemes. Additionally, an equilibrium wallmodel is also employed when the grid resolution near the wall does not suffice. Results are initially presented for a channel flow at Re_τ=950 and Ma=0.08, and further extended to a wallhump at Re=936000 and Ma=0.1. A particular challenge arises when considering adaptation (both in cell refinement h and polynomial order p), which can limit the convergence properties of such models in highorder methods. In this sense, the integral lengthscale approximation (ILSA) model is also investigated, which avoids linking the filter width of the unresolved scales to the grid size.
@conference{Font2022ECCOMAS, author = {Font, B. and Naddei, F. and Lehmkuhl, O.}, title = {Turbulence models assessment using finitevolume and highorder methods for aeronautical applications}, year = {2022}, booktitle = {{ECCOMAS} {C}ongress 2022, Oslo (Norway)} }

Deep learning the spanwiseaveraged wake of a circular cylinderFont, B., Weymouth, G. D., Nguyen, V.T., & Tutty, O. R. (2019). 72nd APS Division of Fluid Dynamics Meeting Abstracts, Seattle (US), L17–005.Numerical simulations of long and flexible cylindrical structures become prohibitive at high Reynolds regimes because of the wide range of spatial and temporal scales that need to be resolved. We propose a new flow decomposition based on the spanwise average of the local threedimensional (3D) strip which provides a twodimensional formulation with additional statistical terms accounting for the 3D fluctuations. The latter unclosed terms are modelled through a convolutional neural network (CNN) trained on a highfidelity dataset. The CNN is designed as a multipleinput multipleoutput autoencoder inspired on image recognition architectures. The convolution operation ensures translational invariance and different inputs are tested aiming to provide a Galilean invariant model. Apriori results display 90% correlation of the predicted turbulent fields and current work involves the aposteriori analysis of the model plus the investigation of the model generalisation for different geometries and flow regimes.
@conference{Font2019APS, author = {Font, B. and Weymouth, G.D. and Nguyen, V.T. and Tutty, O.R.}, title = {Deep learning the spanwiseaveraged wake of a circular cylinder}, year = {2019}, booktitle = {72nd APS Division of Fluid Dynamics Meeting Abstracts, Seattle (US)}, url = {https://meetings.aps.org/Meeting/DFD19/Session/L17.5}, pages = {L17005} }

Turbulence dynamics transition of flow past a circular cylinder and the prediction of vortexinduced forcesFont, B., Weymouth, G. D., Nguyen, V.T., & Tutty, O. R. (2019). 17th European Turbulence Conference, Torino (Italy).We investigate the transition of threedimensional (3D) to twodimensional (2D) turbulence of incompressible viscous flow past a circular cylinder as the span is constricted. The inclusion of a bluff body provides novel information with respect to previous work on free turbulent flow [1, 2, 3]. The coexistance of both turbulence dynamics can be found at the mid wake region for highly anisotropic geometries as shown in figure 1 (left). Both 3D and 2D turbulence (5/3 decay rate and 3 decay rate respectively) are captured on the inertial subrange for the Lz = 0.5 case, where Lz is the cylinder span relative to its diameter. Smallscale 3D structures detach from the wall even on very constricted domains. These structures are rapidly twodimensionalised by the largescale rotation of the Kármán vortices when the span is 50% of the diameter or less. The largescale rotation as a mechanism of twodimensionalisation is in agreement with other studies such as [3, 4]. On the other hand, the constriction of the span induces larger forces on the cylinder as displayed in figure 1 (right). There is a quasilinear relation between the r.m.s value of the lift coefficient CL and the turbulence kinetic energy (TKE). Higher values are found on both parameters as the span is reduced because of the emerging energised 2D vortical structures. Evidencing the strong relation of the forces induced to the cylinder and the turbulence statistics, a regression model is included to provide an a priori analysis given a sufficiently large data set.
@conference{Font2019ETC, author = {Font, B. and Weymouth, G.D. and Nguyen, V.T. and Tutty, O.R.}, title = {Turbulence dynamics transition of flow past a circular cylinder and the prediction of vortexinduced forces}, year = {2019}, booktitle = {17th European Turbulence Conference, Torino (Italy)}, eprint = {https://bfg.github.io/assets/pdf/Font_et_al_2019_Turbulence_dynamics_transition_of_flow_past_a_circular_cylinder_and_the_prediction_of_vortexinduced_forces.pdf} }

A twodimensional model for threedimensional symmetric flowsFont, B., Weymouth, G. D., & Tutty, O. R. (2016). UK Fluids Conference, London (UK).A twodimensional model for threedimensional symmetric laminar flows is described. This model is derived from the incompressible NavierStokes equations using the velocitypressure formulation. By locating the origin of the threedimensional structures on the symmetry plane and applying an appropriate treatment of the threedimensional term remaining in the derived equations an accurate solution of the threedimensional flow at the symmetry plane can be achieved. The backwardfacing step numerical test case is used to test the performance and accuracy of the derived model. Above Re = 400, threedimensional structures arise leading to different primary reattachment lengths for the twodimensional and the threedimensional cases. These structures are located close to the separation point. We show that using a twodimensional transport equation for the responsible threedimensional term would result into a reattachment length close to the threedimensional solution. The direct benefit of this work is a significant reduction of the computational time required to achieve the threedimensional solution of symmetric laminar flows. As a future work, a twodimensional model of threedimensional terms will be explored in the field of turbulence for spatially periodic flows.
@conference{Font2016UKFLUIDS, author = {Font, B. and Weymouth, G.D. and Tutty, O.R.}, title = {A twodimensional model for threedimensional symmetric flows}, year = {2016}, booktitle = {UK Fluids Conference, London (UK)}, eprint = {https://bfg.github.io/assets/pdf/Font_et_al_2016_A_twodimensional_model_for_threedimensional_symmetric_flows.pdf} }
Theses

Modelling of Flow Past Long Cylindrical Structures [PhD thesis]Font, B. (2020). University of Southampton.Turbulent flows are fundamental in engineering and the environment, but their chaotic and threedimensional (3D) nature makes them computationally expensive to simulate. In this work, a dimensionality reduction technique is investigated to exploit flows presenting an homogeneous direction, such as wake flows of extruded twodimensional (2D) geometries. First, we examine the effect of the homogeneous direction span on the wake turbulence dynamics of incompressible flow past a circular cylinder at Re=10^4. It is found that the presence of a solid wall induces 3D structures even in highly constricted domains. The 3D structures are rapidly twodimensionalised by the largescale Kármán vortices if the cylinder span is 50% of the diameter or less, as a result of the span being shorter than the natural wake Mode B instability wavelength. It is also observed that 2D and 3D turbulence dynamics can coexist at certain points in the wake depending on the domain geometric anisotropy. With this physical understanding, a 2D datadriven model that incorporates 3D effects, as found in the 3D wake flow, is presented. The 2D model is derived from a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwiseaveraged Navier–Stokes (SANS) equations. The 3D effects included in the SANS equations are in the form of spanwisestress residual (SSR) terms. The inclusion of the SSR terms in 2D systems modifies the flow dynamics from standard 2D Navier–Stokes to spanwiseaveraged dynamics. A machinelearning (ML) model is employed to provide closure to the SANS equations. In the apriori framework, the ML model yields accurate predictions of the SSR terms, in contrast to a standard eddyviscosity model which completely fails to capture the closure term structures. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shearlayer region, high correlation values are still observed. In the aposteriori analysis, while we find evidence of known stability issues with longtime ML predictions for dynamical systems, the closed SANS equations are still capable of predicting wake metrics and induced forces with errors from 110%. This results in approximately an order of magnitude improvement over standard 2D simulations while reducing the computational cost of 3D simulations by 99.5%.
@thesis{Font2020PhD, author = {Font, B.}, title = {Modelling of Flow Past Long Cylindrical Structures}, year = {2020}, school = {University of Southampton}, publisher = {University of Southampton}, eprint = {https://bfg.github.io/assets/pdf/Font_2020_PhD_Modelling_of_Flow_Past_Long_Cylindrical_Structures.pdf}, type = {PhD thesis} }

HighOrder ShockCapturing Schemes for Micro Shock Tubes [Master’s thesis]Font, B. (2015). Cranfield University.Microfluidics has recently become a popular fluid dynamics branch (Whitesides, 2006). Technology advances have facilitated the manufacturing of microscale devices and, because of this, a parallel interest from the fluid dynamics modelling standpoint has risen. The present thesis investigates the shock tube test case for the millimetre and micrometre scales. At these length scales, noncontinuum effects and wall effects dominate the flow physics associated to the shock wave propagation phenomena. The Minitube2D FORTRAN inhouse code has been further developed to solve the fully compressible NavierStokes (NS) equations in different coordinate systems. The advective fluxes are computed using (very) highorder shock wavecapturing schemes together with approximate Riemann solvers under the Godunovtype methods umbrella with a cellcentred FVM approach. The viscous fluxes are computed using a forwardsbackwards FDM discretisation. Different highorder RungeKutta (RK) time integration methods are considered as well. The Maxwell’s slip and the temperature jump boundary conditions have been implemented to account for the rarefaction effects present in small scale problems. The performance of the MUSCL2 scheme and the WENO5, MPWENO7, MPWENO9 and MPWENO11 schemes is investigated for the Sod shock tube (inviscid) test case. It is found that WENO schemes present a tiny oscillatory behaviour as the order increases even though they fulfil the TVD properties. However, the use of TVD RK methods together with very highorder WENO schemes provided very accurate profiles as well as a reduction of the oscillatory behaviour close to discontinuities. Experimental results from Muntz et al. (1969) are used to validate the 1D NS equations. A correct propagation and dissipation of the shock wave can be observed. The 2D NS equations for the Cartesian and axisymmetric coordinate system are validated with numerical data from Zeitoun et al. (2009) and Kumar et al. (2013) respectively. For Zeitoun’s case, a very accurate agreement of different profiles is shown. The use of the slip and the temperature jump boundary conditions proves the applicability of continuum approaches (NS) for slip flows. Some flows features are also correctly captured in the transitional regime using kinetic models as reference data. Besides, a decoupled temperature transport equation is solved showing a good agreement with the temperature field provided by the energy and the state equations. Thus, the correct implementation of a scalar transport equation introduced to the equations system is validated. For Kumar’s case, a similar temperature profile is obtained along the symmetry axis, even though an offset is appreciated. The turbulence model used by Kumar might introduce additional numerical dissipation resulting into a more attenuated distribution. Finally, scale effects are investigated using Zeitoun’s setup as the baseline case. The influence of the Knudsen number is studied by reducing the initial pressures of the shock tube and the height of the channel. It is found that both actions yield to a severe attenuation of shock wave propagation distance. This decay is more severe under the noslip boundary condition with respect to the Maxwell’s slip one. The influence of the initial pressure ratio is studied as well. As expected, high pressure ratios generate faster shock waves. Hence, the shock propagation attenuation (eventually becoming a compression wave) is more important for low pressure ratios.
@thesis{Font2015Msc, author = {Font, B.}, title = {HighOrder ShockCapturing Schemes for Micro Shock Tubes}, year = {2015}, school = {Cranfield University}, publisher = {Cranfield University}, eprint = {https://bfg.github.io/assets/pdf/Font_2015_MSc_Highorder_Shockcapturing_Schemes_for_Micro_Shock_Tubes.pdf}, type = {Master's thesis} }
Invited Talks
 Fluids AI Special Interest Group series, TU Delft, Netherlands, (2024).
 Julia for HPC minisymposia, JuliaCon2024, Netherlands, (2024). https://juliacon.org/2024/minisymposia/hpc/
 Julia for HPC course, High Performance Computing Center Stuttgart (HLRS), Germany, (2023).
 PPPL Computer Science Department’s Machine Learning seminar, Princeton University, US, (2021).
 Engineering Mind Podcast, (2021). https://youtu.be/d1O3dFgvAP4
 Applied Mathematics in Aerospace Engineering seminar, Universidad Politecnica de Madrid, Spain, (2021).
 Applied Math Colloquium, University North Carolina, US, (2021).
 Ocean Engineering, University Rhode Island, US, (2021).
 Fluid Dynamics Group at the Institute of High Performance Computing (A*STAR), Singapore, (2020).
 Fluid Structure Interactions Group Seminar series, University of Southampton, UK, (2020).
 Fluid Structure Interactions Group Seminar series, University of Southampton, UK, (2017).
Google scholar: Citations = 127, hindex = 6, i10index = 4