A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics

•A purely hyperbolic approach for self-gravitating gas dynamics.•Solve elliptic equation in pseudotime as a hyperbolic system.•Two-way coupled simulations of compressible Euler and hyperbolic gravity equations.•High-order convergence of the multi-physics problem in space and time.•Discontinuous Gale...

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Vydané v:	Journal of computational physics Ročník 442; s. 110467
Hlavní autori:	Schlottke-Lakemper, Michael, Winters, Andrew R., Ranocha, Hendrik, Gassner, Gregor J.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cambridge Elsevier Inc 01.10.2021 Elsevier Science Ltd
Predmet:	Adaptive mesh refinement Cartesian coordinates Compressible Euler equations Computational fluid dynamics Computational physics Convergence Discontinuous Galerkin spectral element method Finite element method Fluid flow Galerkin method Gas dynamics Gravitation Gravitational fields Gravitational instability Gravity Grid refinement (mathematics) Hydrodynamic equations Hydrodynamics Hyperbolic self-gravity Multi-physics simulation Physics Poisson equation Runge-Kutta method Shock capturing Simulation Solvers Adaptive mesh refinement Multi-physics simulation Compressible Euler equations Discontinuous Galerkin spectral element method Hyperbolic self-gravity
ISSN:	0021-9991, 1090-2716, 1090-2716
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Popis
Shrnutí:	•A purely hyperbolic approach for self-gravitating gas dynamics.•Solve elliptic equation in pseudotime as a hyperbolic system.•Two-way coupled simulations of compressible Euler and hyperbolic gravity equations.•High-order convergence of the multi-physics problem in space and time.•Discontinuous Galerkin methods with adaptive mesh refinement and shock capturing. One of the challenges when simulating astrophysical flows with self-gravity is to compute the gravitational forces. In contrast to the hyperbolic hydrodynamic equations, the gravity field is described by an elliptic Poisson equation. We present a purely hyperbolic approach by reformulating the elliptic problem into a hyperbolic diffusion problem, which is solved in pseudotime, using the same explicit high-order discontinuous Galerkin method we use for the flow solution. The flow and the gravity solvers operate on a joint hierarchical Cartesian mesh and are two-way coupled via the source terms. A key benefit of our approach is that it allows the reuse of existing explicit hyperbolic solvers without modifications, while retaining their advanced features such as non-conforming and solution-adaptive grids. By updating the gravitational field in each Runge-Kutta stage of the hydrodynamics solver, high-order convergence is achieved even in coupled multi-physics simulations. After verifying the expected order of convergence for single-physics and multi-physics setups, we validate our approach by a simulation of the Jeans gravitational instability. Furthermore, we demonstrate the full capabilities of our numerical framework by computing a self-gravitating Sedov blast with shock capturing in the flow solver and adaptive mesh refinement for the entire coupled system.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0021-9991 1090-2716 1090-2716
DOI:	10.1016/j.jcp.2021.110467