13 Zentrale Universitätseinrichtungen

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/14

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Institute: search.filters.UBSInstitut.Höchstleistungsrechenzentrum Stuttgart (HLRS)Institute: search.filters.UBSInstitut.Fakultätsübergreifend / Sonstige EinrichtungAuthor: search.filters.author.Gassner, Gregor

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    On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics
    (2023) Ranocha, Hendrik; Winters, Andrew R.; Castro, Hugo Guillermo; Dalcin, Lisandro; Schlottke-Lakemper, Michael; Gassner, Gregor; Parsani, Matteo
    We study a temporal step size control of explicit Runge-Kutta (RK) methods for compressible computational fluid dynamics (CFD), including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler equations. We demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy (CFL) number. Our numerical examples show that the error-based step size control is easy to use, robust, and efficient, e.g., for (initial) transient periods, complex geometries, nonlinear shock capturing approaches, and schemes that use nonlinear entropy projections. We demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases, the open source Julia packages Trixi.jl with OrdinaryDiffEq.jl and the C/Fortran code SSDC based on PETSc.
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    Fourth-order paired-explicit Runge-Kutta methods
    (2025) Doehring, Daniel; Christmann, Lars; Schlottke-Lakemper, Michael; Gassner, Gregor; Torrilhon, Manuel
    In this paper, we extend the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et al. (J Comput Phys 393:465-483, 2019) and Nasab and Vermeire (J Comput Phys 468:111470, 2022) to fourth-order of consistency. Based on the order conditions for partitioned Runge-Kutta methods we motivate a specific form of the Butcher arrays which leads to a family of fourth-order accurate methods. The employed form of the Butcher arrays results in a special structure of the stability polynomials, which needs to be adhered to for an efficient optimization of the domain of absolute stability. We demonstrate that the constructed fourth-order P-ERK methods satisfy linear stability, internal consistency, designed order of convergence, and conservation of linear invariants. At the same time, these schemes are seamlessly coupled for codes employing a method-of-lines approach, in particular without any modifications of the spatial discretization. We demonstrate speedup for single-threaded program executions, shared-memory parallelism, i.e., multi-threaded executions and distributed-memory parallelism with MPI. We apply the multirate P-ERK schemes to inviscid and viscous problems with locally varying wave speeds, which may be induced by non-uniform grids or multiscale properties of the governing partial differential equation. Compared to state-of-the-art optimized standalone methods, the multirate P-ERK schemes allow significant reductions in right-hand-side evaluations and wall-clock time, ranging from up to factors greater than four. A reproducibility repository is provided which enables the reader to examine all results presented in this work.