Schlottke-Lakemper, Michael, Winters, Andrew R., Ranocha, Hendrik 
ORCID: 0000-0002-3456-2277 and Gassner, Gregor J.
(2021).
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics.
J. Comput. Phys., 442.
SAN DIEGO:
ACADEMIC PRESS INC ELSEVIER SCIENCE.
ISSN 1090-2716
Abstract
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.
| Item Type: | Journal Article | ||||||||||||||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-585784 | ||||||||||||||||||||
| DOI: | 10.1016/j.jcp.2021.110467 | ||||||||||||||||||||
| Journal or Publication Title: | J. Comput. Phys. | ||||||||||||||||||||
| Volume: | 442 | ||||||||||||||||||||
| Date: | 2021 | ||||||||||||||||||||
| Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | ||||||||||||||||||||
| Place of Publication: | SAN DIEGO | ||||||||||||||||||||
| ISSN: | 1090-2716 | ||||||||||||||||||||
| Language: | English | ||||||||||||||||||||
| Faculty: | Unspecified | ||||||||||||||||||||
| Divisions: | Unspecified | ||||||||||||||||||||
| Subjects: | no entry | ||||||||||||||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/58578 |
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