arXiv subjects

Andrea Beck

Publications and source records attributed to Andrea Beck.

At least 19 recordsLinked to original sources

arXiv2026

APU-Accelerated Large Eddy Simulation with the Discontinuous Galerkin Solver GAL{\AE}XI

The exascale computing era, driven by heterogeneous GPU architectures, requires a fundamental redesign of traditional CFD solvers to fully leverage those heterogeneous systems. The discontinuous Galerkin spectral element method (DGSEM) provides an ideal foundation for this transition due to its high-order accuracy and local computational stencil. This work presents recent advances in the development and application of the architecture-agnostic DGSEM framework GAL{\AE}XI by linking hardware optimization, software implementation, and physical validation. The performance of GAL{\AE}XI on the AMD MI300A Accelerated Processing Units (APUs) featured on the Hunter supercomputer is analyzed. Specifically, evaluations of the strong and weak scaling performance and the impact of the compute partitioning modes available on the AMD MI300As are performed. Second, the strategy used to integrate the algorithms necessary for wall-modeled large eddy simulations into the GPU-accelerated framework is outlined. Validation of those algorithms is presented in the form of a plane turbulent channel testcase. Finally, the solver is applied to a demanding flow problem in the form of a wall-resolved large eddy simulation of a transonic compressor cascade. The results from this investigation demonstrate the capabilities of GAL{\AE}XI to accurately capture complex shock-wave/turbulent boundary-layer interactions.

physics.flu-dyn↗

arXiv2026

An Architecture-Agnostic High-Order Discontinuous Galerkin Framework for Compressible Flows

With the recent proliferation of heterogeneous, GPU-accelerated supercomputers, high-order computational fluid dynamics (CFD) simulations of complex, turbulent flows are more accessible than ever. To leverage the computing power of these machines, CFD software must adapt. However, complicating the situation is the emerging need to support hardware from multiple GPU vendors. Addressing this need is the GPU-accelerated, discontinuous Galerkin spectral element method (DGSEM) framework GAL{\AE}XI, a high-order, open source, architecture-agnostic toolchain for the study of complex, compressible, turbulent flows on unstructured, hexahedral grids. GPU-accelerated computations with GAL{\AE}XI are possible on GPU hardware by interfacing Fortran source code to the vendor models CUDA C++ for NVIDIA and HIP C++ for AMD. The DGSEM implementation in GAL{\AE}XI was verified using the method of manufactured solutions to rigorously confirm the expected order of convergence. Simulations of a compressible Taylor-Green-Vortex also demonstrated excellent agreement with reference solutions across all supported architectures. GAL{\AE}XI achieved near ideal strong and weak scaling on GPU hardware from both NVIDIA and AMD. In the largest case, GAL{\AE}XI performed a simulation with 67.1 billion degrees of freedom on 65,536 AMD MI250X graphics compute devices with a parallel efficiency of 82.6%. Comparing node-to-node performance, GPU simulations offered speedups between 7.75x and 8.08x over CPU computations in time-to-solution while consuming less than half the energy. To demonstrate GAL{\AE}XI's effectiveness for production-scale simulations, wall-resolved large eddy simulations of the transonic flow past a NACA 64A-110 airfoil and an ONERA OAT15A airfoil under shock buffet conditions were computed.

physics.flu-dyn↗

arXiv2026

h-Adaptive FV Subcell Shock-Capturing for DGSEM on Heterogeneous Curvilinear Meshes

High-order methods offer superior dispersion and dissipation properties compared to low-order schemes but require robust stabilization for discontinuities. To ensure stability, local artificial viscosity is common, but often degrades sub-element resolution. Conversely, subcell resolution preserving limiting strategies such as the finite volume subcell method are typically restricted to uniform topologies, such as purely hexahedral or simplex meshes, or linear elements. This leaves a significant gap in treating the hybrid-element topologies necessary for complex engineering geometries. To bridge this gap, we introduce a robust shock-capturing approach for the discontinuous Galerkin spectral element method on mixed curvilinear meshes containing hexahedral, prismatic, tetrahedral, and pyramid elements. Non-hexahedral elements are handled via collapsed coordinate transformations. The proposed method utilizes an $h$-adaptive finite volume subcell scheme with an arbitrary subcell resolution up to $2\mathcal{N}+1$. Special care is taken to ensure conforming subcell distributions across different element types. Crucially, discrete conservation is proven theoretically and verified numerically, alongside validations for high-order convergence and robust shock capturing. Finally, the method's applicability to complex configurations is demonstrated through a simulation of the flow around a NACA 0012 airfoil.

math.NA↗

arXiv2026

A Provably Robust Multi-Jet Framework applied to Active Flow Control of an Airfoil in Weakly Compressible Flow

Reinforcement learning has by now become well established in finding excellent flow control strategies for a variety of scenarios. Existing literature has focused on using a simple two-jet solution (and variants there-of) or a straightforward mean-centered multi-jet setup. This mean-centering approach is however non-injective in nature, such that distinct action predictions by the actor network can lead to the same implemented jet-intensities. Thus, the potential of true multi-jet setups still remains unexplored. To this end, in this study we first theoretically analyze multi-jet setups, highlighting the aforementioned pitfall and offer a viable alternative. We also derive upper-bounds on the running costs of these setups, and find the proposed approach to have a jet-count-independent maximum running cost (compared to a near-linear scaling for the traditional setup). The mean-centered and proposed multi-jet setups are applied to a variety of flow-configurations, to test performance and learning capabilities. The new formulation proves effective in learning more complex flow-control strategies, coordinating the jets in a sophisticated manner so as to produce favorable outcomes at minimal actuation cost. For the cylinder-in-channel case, this results in drag and total-force suppression to beyond an idealized symmetric case, whereas for the airfoil the separation region is minimized and significant improvements in aerodynamic efficiency are observed (from 53% up to 73% depending on jet configuration). Additionally, we also incorporate some best practices from traditional RL literature to show fast, reproducible and reliable learning, thereby bringing down the upfront training costs. This study thus provides a robust and mathematically grounded approach to multi-jet design and closes a hitherto overlooked theoretical gap.

physics.flu-dyn↗

arXiv2026

Multi-Fidelity Monte-Carlo Estimation of Satellite Drag in Very-Low-Earth Orbit

Very-low-Earth orbit drag uncertainty quantification in the rarefied/transitional Knudsen-number regime requires estimating not only the mean drag coefficient but also higher-order moments under atmospheric variability, which becomes prohibitively expensive when high-fidelity kinetic solvers are required. This work develops a multi-fidelity Monte Carlo (MFMC) estimator for the drag coefficient using a DSMC solver (PICLas) as the high-fidelity model and two free-molecular panel-method variants (ADBSat with Sentman and Cercignani-Lampis-Lord (CLL) gas-surface interaction models) as low-fidelity control variates. We treat E[C_D] and E[C_D^2] as the primary estimation targets and form the physically induced variance only afterwards via Var(C_D)=E[C_D^2]-(E[C_D])^2. High-fidelity reference moments are obtained from long DSMC sequences using objective convergence criteria based on sliding-window stability and 95% confidence intervals. The MFMC implementation is first numerically verified on an analytic toy model with closed-form moments, then assessed on a canonical CubeSat geometry (validation) and on SOAR, GOCE, and CHAMP configurations (verification) under MSIS-derived thermospheric variability and angle-of-attack uncertainty. When low-fidelity correlations are high for both C_D and C_D^2, MFMC reduces the relative RMSE of E[C_D] and E[C_D^2] by factors of several at matched high-fidelity-equivalent cost; improvements for Var(C_D) remain more case-dependent due to cancellation sensitivity. Overall, the study identifies practical drivers (moment correlations, cost ratios, and weight stability) that govern when panel models serve as effective control variates for DSMC-based drag uncertainty quantification.

physics.space-ph↗

arXiv2025

In-Memory Load Balancing for Discontinuous Galerkin Methods on Polytopal Meshes

High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and scalability on modern hardware. The open-source DG framework FLEXI has recently been extended to support DG schemes on general polytopal elements including tetrahedra, prisms, and pyramids. This advancement enables simulations on complex geometries where purely hexahedral meshes are difficult or impossible to generate. However, the use of meshes with heterogeneous element types introduces a workload imbalance, a consequence of the temporal evolution of modal rather than nodal degrees of freedom and the accompanying transformations. In this work, we present a lightweight, system-agnostic in-memory load balancing strategy designed for high-order DG solvers. The method employs high-precision runtime measurements and efficient data redistribution to dynamically reassign mesh elements along a space-filling curve. We demonstrate the effectiveness of the approach through simulations of the Taylor-Green vortex and large-scale parallel runs on the EuroHPC pre-exascale system MareNostrum 5. Results show that the proposed strategy recovers a significant fraction of the lost efficiency on heterogeneous meshes while retaining excellent strong and weak scaling.

math.NA↗

arXiv2025

Evaluating simulation techniques for lubricant distribution in gearboxes

Efficient lubrication is crucial for the performance and durability of high-speed gearboxes, particularly under varying load conditions. Excess lubrication leads to increased churning losses, while insufficient lubrication accelerates wear on contact surfaces. Due to the high rotational speeds involved, direct experimental visualization of lubricant distribution within gearboxes is challenging, making numerical simulations indispensable. Although various modelling approaches exist, a direct comparison that jointly evaluates accuracy and computational efficiency is missing. Furthermore, studies on the computational modelling of highly viscous lubricants such as grease in gearboxes are limited. This study addresses these gaps by comparing two mesh-based Eulerian solvers (OpenFOAM and Ansys-Fluent) and two Lagrangian particle-based solvers (PreonLab and MESHFREE) for oil distribution in gearboxes. Two benchmark cases are considered: one for qualitative assessment and another for quantitative evaluation. OpenFOAM and Ansys-Fluent show good agreement with the experiment data in selected cases, but incur a significant computational cost. PreonLab performs well qualitatively, yet exhibits greater deviation in quantitative predictions. These comparisons provide information for selecting the suitable solver according to specific simulation requirements. Furthermore, the study extends to grease distribution by first validating the solver and then investigating the influence of filling volume and gear speed on the amount of grease deposited on gears. The benchmark cases presented provide a reference framework for evaluating additional solvers in future gearbox lubrication studies.

physics.flu-dyn↗

arXiv2025

SmartFlow: A CFD-solver-agnostic deep reinforcement learning framework for computational fluid dynamics on HPC platforms

Deep reinforcement learning (DRL) is emerging as a powerful tool for fluid-dynamics research, encompassing active flow control, autonomous navigation, turbulence modeling and discovery of novel numerical schemes. We introduce SmartFlow, a CFD-solver-agnostic framework for both single- and multi-agent DRL algorithms that can easily integrate with MPI-parallel CPU and GPU-accelerated solvers. Built on Relexi and SmartSOD2D, SmartFlow uses the SmartSim infrastructure library and our newly developed SmartRedis-MPI library to enable asynchronous, low-latency, in-memory communication between CFD solvers and Python-based DRL algorithms. SmartFlow leverages PyTorch's Stable-Baselines3 for training, which provides a modular, Gym-like environment API. We demonstrate its versatility via three case studies: single-agent synthetic-jet control for drag reduction in a cylinder flow simulated by the high-order FLEXI solver, multi-agent cylinder wake control using the GPU-accelerated spectral-element code SOD2D, and multi-agent wall-model learning for large-eddy simulation with the finite-difference solver CaLES. SmartFlow's CFD-solver-agnostic design and seamless HPC integration is promising to accelerate RL-driven fluid-mechanics studies.

physics.flu-dyn↗

arXiv2025

Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes

Hyperbolic-parabolic partial differential equations are widely used for the modeling of complex, multiscale problems. High-order methods such as the discontinuous Galerkin (DG) scheme are attractive candidates for their numerical approximation. However, high-order methods are prone to instabilities in the presence of underresolved flow features. A popular counter measure to stabilize DG methods is the use of entropy-stable formulations based on summation-by-parts (SBP) operators. The present paper aims to construct a robust and efficient entropy-stable discontinuous Galerkin spectral element method (DGSEM) of arbitrary order on heterogeneous, curvilinear grids composed of triangular and quadrilateral elements or hexahedral, prismatic, tetrahedral and pyramid elements. To the author's knowledge, with the exception of hexahedral and quadrilateral elements, entropy-stable DGSE operators have been constructed exclusively for tetrahedral and triangular meshes. The extension of the DGSEM to more complex element shapes is achieved by means of a collapsed coordinate transformation. Legendre--Gauss quadrature nodes are employed as collocation points in conjunction with a generalized SBP operator and entropy-projected variables. The purely hyperbolic operator is extended to hyperbolic-parabolic problems by the use of a lifting procedure. To circumvent the penalizing time step restriction imposed by the collapsing, modal rather than nodal degrees of freedom are evolved in time, thereby relying on a memory-efficient weight-adjusted approximation to the inverse of the mass matrix. Essential properties of the proposed numerical scheme including free-stream preservation, polynomial and grid convergence as well as entropy conservation / stability are verified. Finally, with the flow around the common research model, the applicability of the presented method to real-world problems is demonstrated.

math.NA↗

arXiv2025

Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks

This work proposes a novel methodology for turbulence modeling in Large Eddy Simulation (LES) based on Graph Neural Networks (GNNs), which embeds the discrete rotational, reflectional and translational symmetries of the Navier-Stokes equations into the model architecture. In addition, suitable invariant input and output spaces are derived that allow the GNN models to be embedded seamlessly into the LES framework to obtain a symmetry-preserving simulation setup. The suitability of the proposed approach is investigated for two canonical test cases: Homogeneous Isotropic Turbulence (HIT) and turbulent channel flow. For both cases, GNN models are trained successfully in actual simulations using Reinforcement Learning (RL) to ensure that the models are consistent with the underlying LES formulation and discretization. It is demonstrated for the HIT case that the resulting GNN-based LES scheme recovers rotational and reflectional equivariance up to machine precision in actual simulations. At the same time, the stability and accuracy remain on par with non-symmetry-preserving machine learning models that fail to obey these properties. The same modeling strategy translates well to turbulent channel flow, where the GNN model successfully learns the more complex flow physics and is able to recover the turbulent statistics and Reynolds stresses. It is shown that the GNN model learns a zonal modeling strategy with distinct behaviors in the near-wall and outer regions. The proposed approach thus demonstrates the potential of GNNs for turbulence modeling, especially in the context of LES and RL.

physics.flu-dyn↗

arXiv2025

Comparison of Entropy Stable Collocation High-Order DG Methods for Compressible Turbulent Flows

High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations. This paper provides a detailed comparison of the effectiveness of entropy stable discontinuous Galerkin methods for the stabilization of compressible (wall-bounded) turbulent flows. For this investigation, an entropy stable discontinuous Galerkin spectral element method is applied on Gauss-Legendre and Gauss-Lobatto nodes. In the compressible regime, an additional stabilization technique for shock capturing based on a convex blending of a low-order finite volume with the high-order discontinuous Galerkin operator is utilized. The present investigation provides a systematic study from convergence tests, to the Taylor-Green vortex and finally to a more intricate turbulent wall-bounded 3D diffuser flow, encompassing both weakly compressible and compressible regimes. The comparison demonstrates that the DGSEM on Gauss-Lobatto nodes is less accurate due to the lower integration accuracy. Conversely, it is faster than the DGSEM on Gauss-Legendre nodes due to a less severe time step restriction and simpler numerical operator. To the author's knowledge, this is the first time for which a comparison of entropy stable DGSEM on Gauss-Lobatto and Gauss-Legendre has been performed for compressible, wall-bounded turbulent flows with separation.

physics.flu-dyn↗

arXiv2025

Entropy stable shock capturing for high-order DGSEM on moving meshes

In this paper, a shock capturing for high-order entropy stable discontinuous Galerkin spectral element methods on moving meshes is proposed using Gauss--Lobatto nodes. The shock capturing is achieved via the convex blending of the high-order scheme with a low-order finite volume subcell operator. The free-stream and convergence properties of the hybrid scheme are demonstrated numerically along with the entropy stability and shock capturing capabilities.

math.NA↗

arXiv2025

Invariant Control Strategies for Active Flow Control using Graph Neural Networks

Reinforcement learning has gained traction for active flow control tasks, with initial applications exploring drag mitigation via flow field augmentation around a two-dimensional cylinder. RL has since been extended to more complex turbulent flows and has shown significant potential in learning complex control strategies. However, such applications remain computationally challenging due to its sample inefficiency and associated simulation costs. This fact is worsened by the lack of generalization capabilities of these trained policy networks, often being implicitly tied to the input configurations of their training conditions. In this work, we propose the use of graph neural networks to address this particular limitation, effectively increasing the range of applicability and getting more value out of the upfront RL training cost. GNNs can naturally process unstructured, threedimensional flow data, preserving spatial relationships without the constraints of a Cartesian grid. Additionally, they incorporate rotational, reflectional, and permutation invariance into the learned control policies, thus improving generalization and thereby removing the shortcomings of commonly used CNN or MLP architectures. To demonstrate the effectiveness of this approach, we revisit the well-established two-dimensional cylinder benchmark problem for active flow control. The RL training is implemented using Relexi, a high-performance RL framework, with flow simulations conducted in parallel using the high-order discontinuous Galerkin framework FLEXI. Our results show that GNN-based control policies achieve comparable performance to existing methods while benefiting from improved generalization properties. This work establishes GNNs as a promising architecture for RL-based flow control and highlights the capabilities of Relexi and FLEXI for large-scale RL applications in fluid dynamics.

cs.LG↗

arXiv2025

Efficient computation of particle-fluid and particle-particle interactions in compressible flow

Particle collisions are the primary mechanism of inter-particle momentum and energy exchange for dense particle-laden flow. Accurate approximation of this collision operator in four-way coupled Euler-Lagrange approaches remains challenging due to the associated computational cost. Adopting a deterministic collision model and a hard-sphere approach eases time step constraints but imposes non-locality on distributed memory architectures, necessitating the inclusion of collision partners from each grid element in the vicinity. Retaining high-order accuracy and parallel efficiency also ties into the correct and compact treatment of the particle-fluid coupling, where adequate kernels are required to effectively project the work of the particles to the Eulerian grid. In this work, we present an efficient particle collision and projection operator based on an MPI+MPI hybrid approach to enable time-resolved and high-order accurate simulations of compressible, four-way coupled particle-laden flows at dense concentrations. A distinct feature of the proposed particle collision algorithm is the efficient calculation of exact binary inter-particle collisions on arbitrary core counts. Combining the particle operator with a hybrid discretization operator based on a high-order discontinuous Galerkin method and a localized low-order finite volume operator allows an accurate treatment of highly compressible particle-laden flows. The approach is extensively validated against a range of benchmark problems. Contrary to literature, the scaling properties are demonstrated on state-of-the-art high performance computing systems. Finally, the proposed algorithm is compatible with unstructured, curved high-order grids which permits the handling of complex geometries as is emphasized by application of the framework to large-scale application cases.

physics.comp-ph↗

arXiv2024

GAL{\AE}XI: Solving complex compressible flows with high-order discontinuous Galerkin methods on accelerator-based systems

This work presents GALAEXI as a novel, energy-efficient flow solver for the simulation of compressible flows on unstructured meshes leveraging the parallel computing power of modern Graphics Processing Units (GPUs). GALAEXI implements the high-order Discontinuous Galerkin Spectral Element Method (DGSEM) using shock capturing with a finite-volume subcell approach to ensure the stability of the high-order scheme near shocks. This work provides details on the general code design, the parallelization strategy, and the implementation approach for the compute kernels with a focus on the element local mappings between volume and surface data due to the unstructured mesh. GALAEXI exhibits excellent strong scaling properties up to 1024 GPUs if each GPU is assigned a minimum of one million degrees of freedom degrees of freedom. To verify its implementation, a convergence study is performed that recovers the theoretical order of convergence of the implemented numerical schemes. Moreover, the solver is validated using both the incompressible and compressible formulation of the Taylor-Green-Vortex at a Mach number of 0.1 and 1.25, respectively. A mesh convergence study shows that the results converge to the high-fidelity reference solution and that the results match the original CPU implementation. Finally, GALAEXI is applied to a large-scale wall-resolved large eddy simulation of a linear cascade of the NASA Rotor 37. Here, the supersonic region and shocks at the leading edge are captured accurately and robustly by the implemented shock-capturing approach. It is demonstrated that GALAEXI requires less than half of the energy to carry out this simulation in comparison to the reference CPU implementation. This renders GALAEXI as a potent tool for accurate and efficient simulations of compressible flows in the realm of exascale computing and the associated new HPC architectures.

cs.MS↗

arXiv2023

Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning

This study proposes a novel method for developing discretization-consistent closure schemes for implicitly filtered Large Eddy Simulation (LES). Here, the induced filter kernel, and thus the closure terms, are determined by the properties of the grid and the discretization operator, leading to additional computational subgrid terms that are generally unknown in a priori analysis. In this work, the task of adapting the coefficients of LES closure models is thus framed as a Markov decision process and solved in an a posteriori manner with Reinforcement Learning (RL). This optimization framework is applied to both explicit and implicit closure models. The explicit model is based on an element-local eddy viscosity model. The optimized model is found to adapt its induced viscosity within discontinuous Galerkin (DG) methods to homogenize the dissipation within an element by adding more viscosity near its center. For the implicit modeling, RL is applied to identify an optimal blending strategy for a hybrid DG and Finite Volume (FV) scheme. The resulting optimized discretization yields more accurate results in LES than either the pure DG or FV method and renders itself as a viable modeling ansatz that could initiate a novel class of high-order schemes for compressible turbulence by combining turbulence modeling with shock capturing in a single framework. All newly derived models achieve accurate results that either match or outperform traditional models for different discretizations and resolutions. Overall, the results demonstrate that the proposed RL optimization can provide discretization-consistent closures that could reduce the uncertainty in implicitly filtered LES.

physics.flu-dyn↗

arXiv2023

Towards Exascale CFD Simulations Using the Discontinuous Galerkin Solver FLEXI

Modern high-order discretizations bear considerable potential for the exascale era due to their high fidelity and the high, local computational load that allows for computational efficiency in massively parallel simulations. To this end, the discontinuous Galerkin (DG) framework FLEXI was selected to demonstrate exascale readiness within the Center of Excellence for Exascale CFD (CEEC) by simulating shock buffet on a three-dimensional wing segment at transsonic flight conditions. This paper summarizes the recent progress made to enable the simulation of this challenging exascale problem. For this, it is first demonstrated that FLEXI scales excellently to over 500 000 CPU cores on HAWK at the HLRS. To tackle the considerable resolution requirements near the wall, a novel wall model is proposed that takes compressibility effects into account and yields decent results for the simulation of a NACA 64A-110 airfoil. To address the shocks in the domain, a finite-volume-based shock capturing method was implemented in FLEXI, which is validated here using the simulation of a linear compressor cascade at supersonic flow conditions, where the method is demonstrated to yield efficient, robust and accurate results. Lastly, we present the TensorFlow-Fortran-Binding (TFFB) as an easy-to-use library to deploy trained machine learning models in Fortran solvers such as FLEXI.

cs.DC↗

arXiv2023

A Viscous and Heat Conducting Ghost Fluid Method for Multi-Fluid Simulations

The ghost fluid method allows a propagating interface to remain sharp during a numerical simulation. The solution of the Riemann problem at the interface provides proper information to determine interfacial fluxes as well as the velocity of the phase boundary. Then considering two-material problems, the initial states of the Riemann problem belong to different fluids, which may have different equations of states. In the inviscid case, the solution of the multi-fluid Riemann problem is an extension of the classical Riemann problem for a single fluid. The jump of the initial states between different fluids generates waves in both fluids and induces a movement of the interface, similar to a contact discontinuity. More subtle is the extension to viscous and heat conduction terms which is the main focus of this paper. We account for the discontinuous coefficients of viscosity and heat conduction at the multi-fluid interface and derive solutions of the Riemann problem for these parabolic terms, from which we can derive parabolic, interfacial fluxes.

physics.flu-dyn↗