arXiv subjects

Holger Foysi

Publications and source records attributed to Holger Foysi.

17 recordsLinked to original sources

arXiv2025

Reduction of Outflow Boundary Influence on Aerodynamic Performance using Neural Networks

The accurate treatment of outflow boundary conditions remains a critical challenge in computational fluid dynamics when predicting aerodynamic forces and/or acoustic emissions. This is particularly evident when employing the lattice Boltzmann method (LBM) as the numerical solution technique, which often suffers from inaccuracies induced by artificial reflections from outflow boundaries. This paper investigates the use of neural networks (NN) to mitigate these adverse boundary effects and enable truncated domain requirements. Two distinct NN-based approaches are proposed: (1) direct reconstruction of unknown particle distribution functions at the outflow boundary; and (2) enhancement of established characteristic boundary conditions (CBC) by dynamically tuning their parameters. The direct reconstruction model was trained on data generated from a 2D flow over a cylindrical obstruction. The drag, lift, and Strouhal number were used to test the new boundary condition. We analyzed results for various Reynolds numbers and restricted domain sizes where it demonstrated significantly improved predictions when compared with the traditional Zou & He boundary condition. To examine the robustness of the NN-based reconstruction, the same condition was applied to the simulation of a NACA0012 airfoil, again providing accurate aerodynamic performance predictions. The neural-enhanced CBC were evaluated on a 2D convected vortex benchmark and showed superior performance in minimizing density errors compared to CBCs with fixed parameters. These findings highlight the potential of NN-integrated boundary conditions to improve accuracy and reduce computational expense of aerodynamic and acoustic emissions simulations with the LBM.

physics.comp-ph↗

arXiv2025

Full Domain Analysis in Fluid Dynamics

Novel techniques in evolutionary optimization, simulation and machine learning allow for a broad analysis of domains like fluid dynamics, in which computation is expensive and flow behavior is complex. Under the term of full domain analysis we understand the ability to efficiently determine the full space of solutions in a problem domain, and analyze the behavior of those solutions in an accessible and interactive manner. The goal of full domain analysis is to deepen our understanding of domains by generating many examples of flow, their diversification, optimization and analysis. We define a formal model for full domain analysis, its current state of the art, and requirements of subcomponents. Finally, an example is given to show what we can learn by using full domain analysis. Full domain analysis, rooted in optimization and machine learning, can be a helpful tool in understanding complex systems in computational physics and beyond.

cs.LG↗

arXiv2024

Supersonic Shear and Wall-Bounded Flows With Body-Fitted Meshes Using the Semi-Lagrangian Lattice Boltzmann Method: Boundary Schemes and Applications

Lattice Boltzmann method (LBM) simulations of incompressible flows are nowadays common and well-established. However, for compressible turbulent flows with strong variable density and intrinsic compressibility effects, results are relatively scarce. Only recently, progress was made regarding compressible LBM, usually applied to simple one and two-dimensional test cases due to the increased computational expense. The recently developed semi-Lagrangian lattice Boltzmann method (SLLBM) is capable of simulating two- and three-dimensional viscous compressible flows. This paper presents bounce-back, thermal, inlet, and outlet boundary conditions new to the method and their application to problems including heated or cooled walls, often required for supersonic flow cases. Using these boundary conditions, the SLLBM's capabilities are demonstrated in various test cases, including a supersonic 2D NACA-0012 airfoil, flow around a 3D sphere, and, to the best of our knowledge, for the first time, the 3D simulation of a supersonic turbulent channel flow at a bulk Mach number of Ma=1.5 and a 3D temporal supersonic compressible mixing layer at convective Mach numbers ranging from Ma=0.3 to Ma=1.2. The results show that the compressible SLLBM is able to adequately capture intrinsic and variable density compressibility effects.

physics.flu-dyn↗

arXiv2024

Machine Learning Enhanced Collision Operator for the Lattice Boltzmann Method Based on Invariant Networks

Integrating machine learning techniques in established numerical solvers represents a modern approach to enhancing computational fluid dynamics simulations. Within the lattice Boltzmann method (LBM), the collision operator serves as an ideal entry point to incorporate machine learning techniques to enhance its accuracy and stability. In this work, an invariant neural network is constructed, acting on an equivariant collision operator, optimizing the relaxation rates of non-physical moments. This optimization enhances robustness to symmetry transformations and ensures consistent behavior across geometric operations. The proposed neural collision operator (NCO) is trained using forced isotropic turbulence simulations driven by spectral forcing, ensuring stable turbulence statistics. The desired performance is achieved by minimizing the energy spectrum discrepancy between direct numerical simulations and underresolved simulations over a specified wave number range. The loss function is further extended to tailor numerical dissipation at high wave numbers, ensuring robustness without compromising accuracy at low and intermediate wave numbers. The NCO's performance is demonstrated using three-dimensional Taylor-Green vortex (TGV) flows, where it accurately predicts the dynamics even in highly underresolved simulations. Compared to other LBM models, such as the BGK and KBC operators, the NCO exhibits superior accuracy while maintaining stability. In addition, the operator shows robust performance in alternative configurations, including turbulent three-dimensional cylinder flow. Finally, an alternative training procedure using time-dependent quantities is introduced. It is based on a reduced TGV model along with newly proposed symmetry boundary conditions. The reduction in memory consumption enables training at higher Reynolds numbers, successfully leading to stable yet accurate simulations.

physics.comp-ph↗

arXiv2023

Efficient Quality Diversity Optimization of 3D Buildings through 2D Pre-optimization

Quality diversity algorithms can be used to efficiently create a diverse set of solutions to inform engineers' intuition. But quality diversity is not efficient in very expensive problems, needing 100.000s of evaluations. Even with the assistance of surrogate models, quality diversity needs 100s or even 1000s of evaluations, which can make it use infeasible. In this study we try to tackle this problem by using a pre-optimization strategy on a lower-dimensional optimization problem and then map the solutions to a higher-dimensional case. For a use case to design buildings that minimize wind nuisance, we show that we can predict flow features around 3D buildings from 2D flow features around building footprints. For a diverse set of building designs, by sampling the space of 2D footprints with a quality diversity algorithm, a predictive model can be trained that is more accurate than when trained on a set of footprints that were selected with a space-filling algorithm like the Sobol sequence. Simulating only 16 buildings in 3D, a set of 1024 building designs with low predicted wind nuisance is created. We show that we can produce better machine learning models by producing training data with quality diversity instead of using common sampling techniques. The method can bootstrap generative design in a computationally expensive 3D domain and allow engineers to sweep the design space, understanding wind nuisance in early design phases.

cs.NE↗

arXiv2022

Comment on 'Lie symmetry analysis of the Lundgren-Monin-Novikov equations for multi-point probability density functions of turbulent flow'

The recent study by Waclawczyk et al. [J. Phys. A: Math. Theor. 50, 175501 (2017)] possesses three shortcomings: (i) The analysis misses a key aspect of the LMN equations which makes their Lie-group symmetry results incomplete. In particular, two essential symmetries will break when including this aspect. (ii) The statements on the constraints regarding the infinite-dimensional symmetry groups are misleading. (iii) The particular symmetries originating solely from the linearity of the LMN hierarchy violate the classical principle of cause and effect and therefore are unphysical. Within this Comment we present a detailed proof to this claim and conclude with the note that the new study by Waclawczyk et al. gives an unrealistic outlook on deriving invariant symmetry solutions for velocity correlations that arise from intermittent processes.

physics.flu-dyn↗

arXiv2021

Lettuce: PyTorch-based Lattice Boltzmann Framework

The lattice Boltzmann method (LBM) is an efficient simulation technique for computational fluid mechanics and beyond. It is based on a simple stream-and-collide algorithm on Cartesian grids, which is easily compatible with modern machine learning architectures. While it is becoming increasingly clear that deep learning can provide a decisive stimulus for classical simulation techniques, recent studies have not addressed possible connections between machine learning and LBM. Here, we introduce Lettuce, a PyTorch-based LBM code with a threefold aim. Lettuce enables GPU accelerated calculations with minimal source code, facilitates rapid prototyping of LBM models, and enables integrating LBM simulations with PyTorch's deep learning and automatic differentiation facility. As a proof of concept for combining machine learning with the LBM, a neural collision model is developed, trained on a doubly periodic shear layer and then transferred to a different flow, a decaying turbulence. We also exemplify the added benefit of PyTorch's automatic differentiation framework in flow control and optimization. To this end, the spectrum of a forced isotropic turbulence is maintained without further constraining the velocity field. The source code is freely available from https://github.com/lettucecfd/lettuce.

physics.comp-ph↗

arXiv2021

Cubature rules for weakly and fully compressible off-lattice Boltzmann methods

Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauss-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauss-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor-Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor-Green vortex flows with Mach numbers Ma={0.5;1.0;1.5;2.0} on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.

physics.comp-ph↗

arXiv2021

High-order semi-Lagrangian kinetic scheme for compressible turbulence

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques, even when the time step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers for the first time to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time step sizes is only dictated by physics, while being decoupled from the spatial discretization.

physics.comp-ph↗

arXiv2021

Aerodynamic sound of turbulent time-developing shear layer as the outcome of the flow linear non-modal instability

The aim of this paper is to substantiate the importance of non-normality of shear flow linear operators and its consequence -- the non-modal dynamics of the perturbations -- in the formation of acoustic wave output of time-developing free shear/mixing layers. Initially, the linear transient dynamics of spatial Fourier harmonics is considered in a 3D homentropic parallel unbounded inviscid constant shear flow which can model the central/body part of the shear layer. The non-modal approach allows to capture the only linear mechanism of the acoustic wave generation -- \textit{the linear vortex-wave mode coupling induced by the shear flow non-normality}. We describe the specific/key features of the generation process that should leave traces on the further dynamics of the generated waves. Thereafter, the results of direct numerical simulations of compressible turbulent time-developing mixing layers for a moderate convective Mach number (specifically, $M_c=0.7$) and simulation boxes $(L_x,L_y,L_z)$ with fixed streamwise and shearwise lengths ($L_x=100, L_y=200$) and different streamwise-spanwise aspect ratios ($L_x/L_z=0.5,1,2$) are presented. The simulations identify the origin of the acoustic wave output: the dominance of a \emph{linear generation process of acoustic waves in the shear layer core region, induced by the flow non-normality}, observable in the near field of acoustic waves emitted by the flow.

physics.flu-dyn↗

arXiv2020

A new class of discontinuous solar wind solutions

A new class of one-dimensional solar wind models is developed within the general polytropic, single-fluid hydrodynamic framework. The particular case of quasi-adiabatic radial expansion with a localized heating source is considered. We consider analytical solutions with continuous Mach number over the entire radial domain while allowing for jumps in the flow velocity, density, and temperature, provided that there exists an external source of energy in the vicinity of the critical point which supports such jumps in physical quantities. This is substantially distinct from both the standard Parker solar wind model and the original nozzle solutions, where such discontinuous solutions are not permissible. We obtain novel sample analytic solutions of the governing equations corresponding to both slow and fast wind.

astro-ph.SR↗

arXiv2020

Semi-Lagrangian lattice Boltzmann method for compressible flows

This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method, the method operates in a static, non-moving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.

physics.comp-ph↗

arXiv2018

On the Stability of Gradient Based Turbulent Flow Control without Regularization

In this paper, we discuss selected adjoint approaches for the turbulent flow control. In particular, we focus on the application of adjoint solvers for the scope of noise reduction, in which flow solutions are obtained by large eddy and direct numerical simulations. Optimization results obtained with round and plane jet configurations are presented. The results indicate that using large control horizons poses a serious problem for the control of turbulent flows due to existence of very large sensitivity values with respect to control parameters. Typically these sensitivities grow in time and lead to arithmetic overflow in the computations. This phenomena is illustrated by a sensitivity study performed with an exact tangent-linear solver obtained by algorithmic differentiation techniques.

math.OC↗

arXiv2016

On the physical inconsistency of a new statistical scaling symmetry in incompressible Navier-Stokes turbulence

A detailed theoretical investigation is given which demonstrates that a recently proposed statistical scaling symmetry is physically void. Although this scaling is mathematically admitted as a unique symmetry transformation by the underlying statistical equations for incompressible Navier-Stokes turbulence on the level of the functional Hopf equation, by closer inspection, however, it leads to physical inconsistencies and erroneous conclusions in the theory of turbulence. The new statistical symmetry is thus misleading in so far as it forms within an unmodelled theory an analytical result which at the same time lacks physical consistency. Our investigation will expose this inconsistency on different levels of statistical description, where on each level we will gain new insights for its non-physical transformation behavior. With a view to generate invariant turbulent scaling laws, the consequences will be finally discussed when trying to analytically exploit such a symmetry. In fact, a mismatch between theory and numerical experiment is conclusively quantified. We ultimately propose a general strategy on how to not only track unphysical statistical symmetries, but also on how to avoid generating such misleading invariance results from the outset. All the more so as this specific study on a physically inconsistent scaling symmetry only serves as a representative example within the broader context of statistical invariance analysis. In this sense our investigation is applicable to all areas of statistical physics in which symmetries get determined in order to either characterize complex dynamical systems, or in order to extract physically useful and meaningful information from the underlying dynamical process itself.

physics.flu-dyn↗

arXiv2016

A critical examination of the statistical symmetries admitted by the Lundgren-Monin-Novikov hierarchy of unconfined turbulence

We present a critical examination of the recent article by Waclawczyk et al. (2014) which proposes two new statistical symmetries in the classical theory for turbulent hydrodynamic flows. We first show that both symmetries are unphysical in that they induce inconsistencies due to violating the principle of causality. In addition, they must get broken in order to be consistent with all physical constraints naturally arising in the statistical Lundgren-Monin-Novikov (LMN) description of turbulence. As a result, we state that besides the well-known classical symmetries of the LMN equations no new statistical symmetries exist. Yet, aside from this particular issue, the article by Waclawczyk et al. (2014) is flawed in more than one respect, ranging from an incomplete proof, to a self-contradicting statement up to an incorrect claim. All these aspects will be listed, discussed and corrected, thus obtaining a completely opposite conclusion in our study than the article by Waclawczyk et al. (2014) is proposing.

physics.flu-dyn↗

arXiv2016

Is the log-law a first principle result from Lie-group invariance analysis?

The invariance method of Lie-groups in the theory of turbulence carries the high expectation of being a first principle method for generating statistical scaling laws. The purpose of this comment is to show that this expectation has not been met so far. In particular for wall-bounded turbulent flows, the prospects for success are not promising in view of the facts we will present herein. Although the invariance method of Lie-groups is able to generate statistical scaling laws for wall-bounded turbulent flows, like the log-law for example, these invariant results yet not only fail to fulfil the basic requirements for a first principle result, but also are strongly misleading. The reason is that not the functional structure of the log-law itself is misleading, but that its invariant Lie-group based derivation yielding this function is what is misleading. By revisiting the study of Oberlack (2001) we will demonstrate that all Lie-group generated scaling laws derived therein do not convince as first principle solutions. Instead, a rigorous derivation reveals complete arbitrariness rather than uniqueness in the construction of invariant turbulent scaling laws. Important to note here is that the key results obtained in Oberlack (2001) are based on several technical errors, which all will be revealed, discussed and corrected. The reason and motivation why we put our focus solely on Oberlack (2001) is that it still marks the core study and central reference point when applying the method of Lie-groups to turbulence theory. Hence it is necessary to shed the correct light onto that study. Nevertheless, even if the method of Lie-groups in its full extent is applied and interpreted correctly, strong natural limits of this method within the theory of turbulence exist, which, as will be finally discussed, constitute insurmountable obstacles in the progress of achieving a significant breakthrough.

physics.flu-dyn↗

arXiv2016

A note on the notion "statistical symmetry"

A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short note is to provide this missing information and to clarify this notion on the basis of a few instructive examples.

physics.flu-dyn↗