Journal Articles

1. WaterLily.jl: A differentiable and backend-agnostic Julia solver to simulate incompressible viscous flow and dynamic bodies
   Weymouth, G. D., & Font, B. (2024, submitted). Abstract BibTeX ePrint
   Integrating computational fluid dynamics (CFD) software into optimization and machine-learning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible high-level languages. In this work, we introduce WaterLily.jl: an open-source 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 backend-agnostic (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 speed-up using CUDA kernels resulting in a cost of 1.44 nanoseconds per DOF and time step. This leads to comparable performance with low-level CFD solvers written in C and Fortran on research-scale problems, opening up exciting possible future applications on the cutting edge of machine-learning research.

   @article{WeymouthFont2024,
     author = {Weymouth, G.D. and Font, B.},
     year = {2024, submitted},
     title = {{WaterLily.jl: A differentiable and backend-agnostic Julia solver to simulate incompressible viscous flow and dynamic bodies}},
     eprint = {https://arxiv.org/pdf/2407.16032}
   }
   

2. Deep reinforcement learning for active flow control in a turbulent separation bubble
   Font, B., Alcántara-Ávila, F., Rabault, J., Vinuesa, R., & Lehmkuhl, O. (2024, submitted). BibTeX ePrint

   @article{Font2024b,
     author = {Font, B. and Alcántara-Ávila, 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/rs-4565966/v1.pdf?c=1719317674000}
   }
   

3. Active flow control for drag reduction through multi-agent reinforcement learning on a turbulent cylinder at Re_D=3900
   Suárez, P., Álcantara-Ávila, F., Rabault, J., Miró, A., Font, B., Lehmkuhl, O., & Vinuesa, R. (2024, submitted). Abstract BibTeX ePrint
   This study presents novel active-flow-control (AFC) strategies aimed at achieving drag reduction for a three-dimensional 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 zero-net-mass-flux jet pairs, distributed on the top and bottom surfaces, which define the AFC setup. The method is based on the coupling between a computational-fluid-dynamics solver and a multi-agent reinforcement-learning (MARL) framework using the proximal-policy-optimization 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 Álcantara-Ávila, F. and Rabault, J. and Miró, A. and Font, B. and Lehmkuhl, O. and Vinuesa, R.},
     title = {Active flow control for drag reduction through multi-agent reinforcement learning on a turbulent cylinder at {$Re_D=3900$}},
     publisher = {arXiv},
     year = {2024, submitted}
   }
   

4. Flow control of three-dimensional cylinders transitioning to turbulence via multi-agent reinforcement learning
   Suárez, P., Álcantara-Ávila, F., Rabault, J., Miró, A., Font, B., Lehmkuhl, O., & Vinuesa, R. (2024, submitted). Abstract BibTeX ePrint
   Designing active-flow-control (AFC) strategies for three-dimensional (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 high-dimensional 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 zero-net-mass-flux jets positioned on the top and bottom surfaces, aligned into two slots. The method relies on coupling the computational-fluid-dynamics solver with a multi-agent reinforcement-learning (MARL) framework based on the proximal-policy-optimization algorithm. MARL offers several advantages: it exploits local invariance, adaptable control across geometries, facilitates transfer learning and cross-application 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 MARL-based framework represents the first time where training is conducted in 3D cylinders. This breakthrough paves the way for conducting AFC on progressively more complex turbulent-flow configurations.

   @article{Suarez2024a,
     author = {Suárez, P. and Álcantara-Ávila, F. and Rabault, J. and Miró, A. and Font, B. and Lehmkuhl, O. and Vinuesa, R.},
     title = {Flow control of three-dimensional cylinders transitioning to turbulence via multi-agent reinforcement learning},
     eprint = {https://arxiv.org/pdf/2405.17655},
     publisher = {arXiv},
     year = {2024, submitted}
   }
   

5. Hydrothermal liquefaction of Spanish crude olive pomace for biofuel and biochar production
   Cutz, L., Misara, S., Font, B., Al-Naji, M., & de Jong, W. (2024, submitted). BibTeX

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

6. A data-driven non-equilibrium wall model for LES of transitional flows
   Radhakrishnan, S., Calafell, J., Miró, A., Font, B., & Lehmkuhl, O. (2024). International Journal of Numerical Methods for Heat & Fluid Flow. BibTeX DOI ePrint

   @article{Radhakrishnan2024,
     author = {Radhakrishnan, S. and Calafell, J. and Mir\'{o}, A. and Font, B. and Lehmkuhl, O.},
     year = {2024},
     title = {A data-driven non-equilibrium wall model for {LES} of transitional flows},
     doi = {10.1108/HFF-11-2023-0710},
     journal = {International Journal of Numerical Methods for Heat \& Fluid Flow},
     eprint = {https://www.emerald.com/insight/content/doi/10.1108/HFF-11-2023-0710/full/pdf?title=data-driven-wall-modeling-for-les-involving-non-equilibrium-boundary-layer-effects}
   }
   

7. Deep reinforcement learning for flow control exploits different physics for increasing Reynolds number regimes
   Varela, P., Suárez, P., Alcántara-Ávila, F., Miró, A., Rabault, J., Font, B., García-Cuevas, L. M., Lehmkuhl, O., & Vinuesa, R. (2022). Actuators, 11(12). Abstract BibTeX DOI ePrint
   The increase in emissions associated with aviation requires deeper research into novel sensing and flow-control strategies to obtain improved aerodynamic performances. In this context, data-driven 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. Two-dimensional 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 pressure-drag 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 flow-control 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 high-frequency actuation. A cross-application 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 nature-different flow, which would only admits a high-frequency 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 Alcántara-Ávila, F. and Mir\'{o}, A. and Rabault, J. and Font, B. and García-Cuevas, 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},
     article-number = {359},
     doi = {10.3390/act11120359},
     eprint = {https://www.mdpi.com/2076-0825/11/12/359/pdf?version=1669977565}
   }
   

8. Deep learning of the spanwise-averaged Navier–Stokes equations
   Font, B., Weymouth, G. D., Nguyen, V.-T., & Tutty, O. R. (2021). Journal of Computational Physics, 434, 110199. Abstract BibTeX DOI ePrint
   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 strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier–Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori 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 shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori 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 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D 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 spanwise-averaged {N}avier--{S}tokes equations},
     journal = {Journal of Computational Physics},
     volume = {434},
     pages = {110199},
     issn = {0021-9991},
     doi = {10.1016/j.jcp.2021.110199},
     eprint = {https://arxiv.org/pdf/2008.07528}
   }
   

9. Span effect on the turbulence nature of flow past a circular cylinder
   Font, B., Weymouth, G. D., Nguyen, V.-T., & Tutty, O. R. (2019). Journal of Fluid Mechanics, 878, 306–323. Abstract BibTeX DOI ePrint
   Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2D) and three-dimensional (3D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an important impact on the cross-over 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 small-scale structures detach from the walls. Additionally, the natural large-scale rotation of the Kármán vortices rapidly two-dimensionalises 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 small-scale 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 = {306--323},
     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}
   }
   

Peer-reviewed Symposium Proceedings

1. Active flow control of a turbulent separation bubble through deep reinforcement learning
   Font, B., Alcántara-Ávila, F., Rabault, J., Vinuesa, R., & Lehmkuhl, O. (2024). Journal of Physics: Conference Series, 2753(1), 012022. Abstract BibTeX DOI ePrint
   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 zero-net-mas-flux (ZNMF) periodic control is able to reduce the TSB by 15.7%. On the other hand, the DRL-based 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 Reynolds-number flow that has been successfully controlled using DRL to this date. In future work, these results will be scaled to well-resolved large-eddy simulation grids. Furthermore, we provide details of our open-source CFD–DRL framework suited for the next generation of exascale computing machines.

   @inproceedings{Font2024a,
     author = {Font, B. and Alcántara-Ávila, 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 = {10.1088/1742-6596/2753/1/012022},
     eprint = {https://arxiv.org/pdf/2403.20295}
   }
   

2. φ–flow: A novel physics-constrained architecture to enforce incompressibility and boundary conditions for fast and accurate flow predictions
   Cabral, M., Font, B., & Weymouth, G. D. (2024). 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics. Abstract BibTeX DOI
   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 study, a formulation that, by construction, enforces flow incompressibility and respects the invariance of physical laws across different unit systems is introduced. We demonstrate that this approach can achieve performance improvements of up to 100 times compared to purely data-driven methods, all while maintaining fidelity to other crucial physical quantities. Moreover, we show that for canonical flow test cases, such a physics-constrained model can yield accurate results even with training datasets as small as a few hundred points and neural networks containing only a handful of neurons. It is also shown, however, that physics-constrained machine learning models are not silver bullets out of the box, and require careful consideration in their application and integration with other constraints. Specifically, this study addresses how a problem that is mathematically simple may not necessarily be straightforward in machine learning terms, and discusses ongoing efforts to bridge this gap. We conclude by discussing the place of physics-constrained machine learning models within a landscape primarily dominated by physics-informed approaches, in particular in the context of real-world problems where data and computational resources are often limited.

   @inproceedings{Cabral2024ECCOMAS,
     series = {WCCM 2024},
     title = {$\phi$--flow: {A} novel physics-constrained architecture to enforce incompressibility and boundary conditions for fast and accurate flow predictions},
     doi = {10.23967/eccomas.2024.002},
     booktitle = {16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics},
     publisher = {CIMNE},
     author = {Cabral, M. and Font, B. and Weymouth, G.D.},
     year = {2024},
     collection = {WCCM 2024}
   }
   

3. Towards active flow control strategies through deep reinforcement learning
   Montalà, R., Font, B., Lehmkuhl, O., Vinuesa, R., & Rodriguez, I. (2024). 16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics. Abstract BibTeX DOI ePrint
   This paper presents a deep reinforcement learning (DRL) framework for active flow control (AFC) to reduce drag in aerodynamic bodies. Tested on a 3D cylinder at Re=100, the DRL approach achieved a 9.32% drag reduction and a 78.4% decrease in lift oscillations by learning advanced actuation strategies. The methodology integrates a CFD solver with a DRL model using an in-memory database for efficient communication between the two instances, making it scalable to more complex flows and higher Reynolds numbers.

   @inproceedings{Montala2024ECCOMAS,
     series = {WCCM 2024},
     title = {Towards active flow control strategies through deep reinforcement learning},
     booktitle = {16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational Mechanics},
     publisher = {CIMNE},
     doi = {10.23967/eccomas.2024.115},
     author = {Montalà, R. and Font, B. and Lehmkuhl, O. and Vinuesa, R. and Rodriguez, I.},
     year = {2024},
     collection = {WCCM 2024},
     eprint = {https://arxiv.org/pdf/2411.05536}
   }
   

4. A data-driven wall-shear stress model for LES using gradient boosted decision trees
   Radhakrishnan, S., Gyamfi, L. A., Miró, A., Font, B., Calafell, J., & Lehmkuhl, O. (2021). ISC High Performance Computing Conference, 105–121. Abstract BibTeX DOI ePrint
   With the recent advances in machine learning, data-driven 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 wall-mounted 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 data-driven 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 data-driven wall-shear stress model for LES using gradient boosted decision trees},
     booktitle = {ISC High Performance Computing Conference},
     publisher = {Springer International Publishing},
     pages = {105--121},
     isbn = {978-3-030-90539-2},
     doi = {10.1007/978-3-030-90539-2_7},
     eprint = {https://upcommons.upc.edu/bitstream/handle/2117/358666/Contribution_TitleSupported_by_organization_x___2_.pdf?sequence=6&isAllowed=y}
   }
   

5. Turbulent wake prediction using deep convolutional neural networks
   Font, B., Weymouth, G. D., Nguyen, V.-T., & Tutty, O. R. (2020). 33rd Symposium on Naval Hydrodynamics. Abstract BibTeX ePrint
   A machine-learning 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 turbulent-viscosity hypothesis are not capable of modelling the non-linear relationship between the mean quantities and the target turbulent fields. Instead, different multiple-input multiple-output auto-encoder convolutional neural networks are explored in this work to develop a data-driven closure. A detailed hyper-parameter study is completed including network architecture, loss functions and input sets, among others. A-priori 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 physics-based constraints ideas to provide more stable data-driven 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://b-fg.github.io/assets/pdf/Font_et_al_2020_Turbulent_wake_prediction_using_deep_convolutional_neural_networks.pdf}
   }
   

Conference Proceedings

1. WaterLily.jl: A differentiable fluid simulator in Julia with fast heterogeneous execution
   Weymouth, G. D., & Font, B. (2023). In ParCFD 2023, Cuenca (Ecuador). Abstract BibTeX ePrint
   Integrating computational fluid dynamics (CFD) software into optimization and machine-learning frameworks is hampered by the rigidity of classic computational languages and the slow performance of more flexible high-level languages. WaterLily.jl is an open-source incompressible viscous flow solver written in the Julia language. The small code base is multi-dimensional, multi-platform and backend-agnostic (serial CPU, multi-threaded, & GPU execution). The simulator is differentiable and uses automatic-differentiation 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 speed-up using CUDA kernels. This leads to comparable performance with Fortran solvers on many research-scale problems opening up exciting possible future applications on the cutting edge of machine-learning 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}
   }
   

2. Active flow control for three-dimensional cylinders through deep reinforcement learning
   Suárez, P., Alcántara-Ávila, F., Miró, A., Rabault, J., Font, B., Lehmkuhl, O., & Vinuesa, R. (2023). In 14th International ERCOFTAC Symposium on Engineering, Turbulence, Modelling and Measurements. Abstract BibTeX ePrint
   This paper presents for the first time successful results of active flow control with multiple independently controlled zero-net-mass-flux synthetic jets. The jets are placed on a three-dimensional cylinder along its span with the aim of reducing the drag coefficient. The method is based on a deep-reinforcement-learning framework that couples a computational-fluid-dynamics solver with an agent using the proximal-policy-optimization algorithm. We implement a multi-agent reinforcement- learning framework which offers numerous advantages: it exploits local invariants, makes the control adaptable to different geometries, facilitates transfer learning and cross-application of agents and results in significant training speedup. In this contribution we report significant drag reduction after applying the DRL-based control in three different configurations of the problem.

   @proceedings{Suarez2023ERCOFTAC,
     author = {Suárez, P. and Alcántara-Ávila, F. and Mir\'{o}, A. and Rabault, J. and Font, B. and Lehmkuhl, O. and Vinuesa, R.},
     title = {Active flow control for three-dimensional 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}
   }
   

3. Analysis of two-dimensional and three-dimensional wakes of long circular cylinders
   Font, B., Weymouth, G. D., & Tutty, O. R. (2017). In OCEANS 2017. IEEE. Abstract BibTeX DOI ePrint
   The wake behind a bluff body constitutes an intrinsically three-dimensional flow and it is known that two-dimensional simulations yield to an unphysical prediction of the body forces because of the nature of the two-dimensional Navier-Stokes equations. However, three-dimensional 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 two-dimensional and three-dimensional 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{Font2017OCEANS,
     doi = {10.1109/oceanse.2017.8084904},
     year = {2017},
     publisher = {{IEEE}},
     author = {Font, B. and Weymouth, G.D. and Tutty, O.R.},
     title = {Analysis of two-dimensional and three-dimensional 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}
   }
   

Theses

1. Modelling of Flow Past Long Cylindrical Structures [PhD thesis]
   Font, B. (2020). University of Southampton. Abstract BibTeX ePrint
   Turbulent flows are fundamental in engineering and the environment, but their chaotic and three-dimensional (3-D) 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 two-dimensional (2-D) 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 3-D structures even in highly constricted domains. The 3-D structures are rapidly two-dimensionalised by the large-scale 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 2-D and 3-D turbulence dynamics can coexist at certain points in the wake depending on the domain geometric anisotropy. With this physical understanding, a 2-D data-driven model that incorporates 3-D effects, as found in the 3-D wake flow, is presented. The 2-D model is derived from a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier–Stokes (SANS) equations. The 3-D effects included in the SANS equations are in the form of spanwise-stress residual (SSR) terms. The inclusion of the SSR terms in 2-D systems modifies the flow dynamics from standard 2-D Navier–Stokes to spanwise-averaged dynamics. A machine-learning (ML) model is employed to provide closure to the SANS equations. In the a-priori framework, the ML model yields accurate predictions of the SSR terms, in contrast to a standard eddy-viscosity 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 shear-layer region, high correlation values are still observed. In the a-posteriori analysis, while we find evidence of known stability issues with long-time ML predictions for dynamical systems, the closed SANS equations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D 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://b-fg.github.io/assets/pdf/Font_2020_PhD_Modelling_of_Flow_Past_Long_Cylindrical_Structures.pdf},
     type = {PhD thesis}
   }
   

2. High-Order Shock-Capturing Schemes for Micro Shock Tubes [Master’s thesis]
   Font, B. (2015). Cranfield University. Abstract BibTeX ePrint
   Microfluidics has recently become a popular fluid dynamics branch (Whitesides, 2006). Technology advances have facilitated the manufacturing of micro-scale 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, non-continuum effects and wall effects dominate the flow physics associated to the shock wave propagation phenomena. The Minitube2D FORTRAN in-house code has been further developed to solve the fully compressible Navier-Stokes (N-S) equations in different coordinate systems. The advective fluxes are computed using (very) high-order shock wave-capturing schemes together with approximate Riemann solvers under the Godunov-type methods umbrella with a cell-centred FVM approach. The viscous fluxes are computed using a forwards-backwards FDM discretisation. Different high-order Runge-Kutta (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 high-order 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 N-S equations. A correct propagation and dissipation of the shock wave can be observed. The 2D N-S 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 (N-S) 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 set-up 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 no-slip 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 = {High-Order Shock-Capturing Schemes for Micro Shock Tubes},
     year = {2015},
     school = {Cranfield University},
     publisher = {Cranfield University},
     eprint = {https://b-fg.github.io/assets/pdf/Font_2015_MSc_High-order_Shock-capturing_Schemes_for_Micro_Shock_Tubes.pdf},
     type = {Master's thesis}
   }
   

Invited Talks

1. Interdisciplinary Scientific Computing Laboratory, Pennsylvania State University, US, (2024). https://juliacon.org/2024/minisymposia/hpc/
2. Fluids AI Special Interest Group series, TU Delft, Netherlands, (2024).
3. Julia for HPC minisymposia, JuliaCon2024, Netherlands, (2024). https://juliacon.org/2024/minisymposia/hpc/
4. Julia for HPC course, High Performance Computing Center Stuttgart (HLRS), Germany, (2023).
5. PPPL Computer Science Department’s Machine Learning seminar, Princeton University, US, (2021).
6. Engineering Mind Podcast, (2021). https://youtu.be/d1O3dFgvAP4
7. Applied Mathematics in Aerospace Engineering seminar, Universidad Politecnica de Madrid, Spain, (2021).
8. Applied Math Colloquium, University North Carolina, US, (2021).
9. Ocean Engineering, University Rhode Island, US, (2021).
10. Fluid Dynamics Group at the Institute of High Performance Computing (A*STAR), Singapore, (2020).
11. Fluid Structure Interactions Group Seminar series, University of Southampton, UK, (2020).
12. Fluid Structure Interactions Group Seminar series, University of Southampton, UK, (2017).