06 Fakultät Luft- und Raumfahrttechnik und Geodäsie
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/7
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Item Open Access A time-accurate inflow coupling for zonal LES(2023) Blind, Marcel P.; Kleinert, Johannes; Lutz, Thorsten; Beck, AndreaGenerating turbulent inflow data is a challenging task in zonal large eddy simulation (zLES) and often relies on predefined DNS data to generate synthetic turbulence with the correct statistics. The more accurate, but more involved alternative is to use instantaneous data from a precursor simulation. Using instantaneous data as an inflow condition allows to conduct high fidelity simulations of subdomains of, e.g. an aircraft including all non-stationary or rare events. In this paper, we introduce a toolchain that is capable of interchanging highly resolved spatial and temporal data between flow solvers with different discretization schemes. To accomplish this, we use interpolation algorithms suitable for scattered data in order to interpolate spatially. In time, we use one-dimensional interpolation schemes for each degree of freedom. The results show that we can get stable simulations that map all flow features from the source data into a new target domain. Thus, the coupling is capable of mapping arbitrary data distributions and formats into a new domain while also recovering and conserving turbulent structures and scales. The necessary time and space resolution requirements can be defined knowing the resolution requirements of the used numerical scheme in the target domain.Item Open Access A reinforcement learning based slope limiter for second‐order finite volume schemes(2023) Schwarz, Anna; Keim, Jens; Chiocchetti, Simone; Beck, AndreaHyperbolic equations admit discontinuities in the solution and thus adequate and physically sound numerical schemes are necessary for their discretization. Second‐order finite volume schemes are a popular choice for the discretization of hyperbolic problems due to their simplicity. Despite the numerous advantages of higher‐order schemes in smooth regions, they fail at strong discontinuities. Crucial for the accurate and stable simulation of flow problems with discontinuities is the adequate and reliable limiting of the reconstructed slopes. Numerous limiters have been developed to handle this task. However, they are too dissipative in smooth regions or require empirical parameters which are globally defined and test case specific. Therefore, this paper aims to develop a new slope limiter based on deep learning and reinforcement learning techniques. For this, the proposed limiter is based on several admissibility constraints: positivity of the solution and a relaxed discrete maximum principle. This approach enables a slope limiter which is independent of a manually specified global parameter while providing an optimal slope with respect to the defined admissibility constraints. The new limiter is applied to several well‐known shock tube problems, which illustrates its broad applicability and the potential of reinforcement learning in numerics.Item Open Access A low Mach number IMEX flux splitting for the level set ghost fluid method(2021) Zeifang, Jonas; Beck, AndreaConsidering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are presented. As acoustic phenomena often play a minor role in such applications, classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction. In this work, a novel scheme based on a specific level set ghost fluid method and an implicit-explicit (IMEX) flux splitting is proposed to overcome this timestep restriction. A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface. In this part of the domain, the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases. It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method. Applications to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.Item Open Access High order discontinuous Galerkin methods for the simulation of multiscale problems(2015) Beck, Andrea; Munz, Claus-Dieter (Prof. Dr.)This work provides a contribution to the accurate, stable and efficient numerical simulation of hydrodynamic non-linear multiscale problems with high order discretizations. Due to their wide range of spatial and temporal scale, these types of problems demand not only highly accurate and efficient numerical discretization schemes, but also careful code design with regards to supercomputing architectures. Still, as a rule, even for the most sophisticated algorithms and hardware, a full resolution of all occurring scales remains infeasible. Thus, an approximate solution with drastically reduced number of degrees of freedom is sought, which retains the most important characteristics of the full solution. This solution is obtained by solving a truncated multiscale problem, supplemented by a suitable modeling strategy for the omitted scales and their interaction with the truncated solution. This approach is only meaningful if the resolvable scales determine the mean solution features accurately, and if the non-resolved scales show some form of universality behavior, which allows the derivation of meaningful models. Hydrodynamic turbulence is one example of these types of problems. In this work, two frameworks for the numerical solution of the compressible Navier-Stokes equations are presented: A self-developed Fourier pseudo-spectral solver, and a co-developed framework based on the Discontinuous Galerkin Spectral Element Method (DGSEM). Both discretization schemes are highly efficient for the resolution of multiscale problems as they – due to their spectral character – exhibit very low approximation errors over a wide range of scales, and thus return a very high resolution capability per invested degree of freedom. Since DGSEM is based on the variational form of the governing equations, it allows an element-based discretization of the computational domain, which in turn leads to superior parallelization and the possibility for flexible, unstructured meshes. These features make it attractive for the full resolution of turbulence in a Direct Numerical Simulation (DNS) approach and – as demonstrated in this work – highly competitive when compared to other discretization strategies. These favorable discretization properties carry over into the under-resolved situation (Large Eddy Simulation, LES), where a lower-dimensional version of the problem is solved numerically. However, depending on the discretization of the scale-producing mechanism, its truncation can introduce a self-feeding error into the solution, that can lead to a global instability. The source and effects of these aliasing errors are investigate in this work. Strategies for countering or avoiding it are presented, and the code framework is extended accordingly. These strategies are compared and evaluated, showing that only the exact quadrature of the non-linear terms recovers the favorable approximation properties and thus the efficiency of the spectral approach. With this discretization strategy, it is shown that high order DGSEM can outperform established, lower-order LES formulations in terms of accuracy per invested degree of freedom for challenging test cases at moderate Reynolds number turbulence. Extension to higher Reynolds numbers necessitates the introduction of some form of closure for the un-resolved scales, due to the increase in the truncation error. Aspects of two modeling approaches are discussed: An implicit modeling strategy for DGSEM can be based on the modification of the dissipation introduced by the inter-cell fluxes. The addition of an explicit modeling term which provides a subgrid dissipation mechanism raises the question whether de-aliasing remains essential in that situation. The de-aliasing strategy is revisited, and its interactions with an explicit closure model are examined. It is shown that only through a proper de-aliasing mechanism, the superior scale-resolving capabilities of the scheme can be recovered, and that a decoupling of explicit model and numerics is imperative. Through these investigations, a consistent strategy for stable and accurate DNS and LES of turbulent flows with high order DGSEM has been established. As an outlook, further research strategies into LES modeling should take full advantage of the spectral character of DGSEM, and the associated scale range resolved within each element can be exploited in both an implicit as well as explicit closure approach.Item Open Access A p-adaptive discontinuous Galerkin method with hp-shock capturing(2022) Mossier, Pascal; Beck, Andrea; Munz, Claus-DieterIn this work, we present a novel hybrid Discontinuous Galerkin scheme with hp-adaptivity capabilities for the compressible Euler equations. In smooth regions, an efficient and accurate discretization is achieved via local p-adaptation. At strong discontinuities and shocks, a finite volume scheme on an h-refined element-local subgrid gives robustness. Thus, we obtain a hp-adaptive scheme that exploits both the high convergence rate and efficiency of a p-adaptive high order scheme as well as the stable and accurate shock capturing abilities of a low order finite volume scheme, but avoids the inherent resolution loss through h-refinement. A single a priori indicator, based on the modal decay of the local polynomial solution representation, is used to distinguish between discontinuous and smooth regions and control the p-refinement. Our method is implemented as an extension to the open source software FLEXI. Hence, the efficient implementation of the method for high performance computers was an important criterion during the development. The efficiency of our adaptive scheme is demonstrated for a variety of test cases, where results are compared against non adaptive simulations. Our findings suggest that the proposed adaptive method produces comparable or even better results with significantly less computational costs.