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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:442

Article

Schlottke-Lakemper, Michael^1,2  Winters, Andrew R.³  Ranocha, Hendrik^4,5  Gassner, Gregor J.^1,2 

[1] Univ Cologne, Dept Math & Comp Sci, Cologne, Germany

[2] Univ Cologne, Ctr Data & Simulat Sci, Cologne, Germany

[3] Linkoping Univ, Dept Math, Appl Math, Linkoping, Sweden

[4] King Abdullah Univ Sci & Technol KAUST, Comp Elect & Math Sci & Engn Div CEMSE, Thuwal, Saudi Arabia

[5] Univ Munster, Appl Math Munster, Munster, Germany

关键词: Discontinuous Galerkin spectral element method;    Multi-physics simulation;    Adaptive mesh refinement;    Compressible Euler equations;    Hyperbolic self-gravity;   

DOI  :  10.1016/j.jcp.2021.110467

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free