Universität zu Köln

Schlottke-Lakemper, Michael, Winters, Andrew R., Gassner, Gregor J. and Ranocha, Hendrik (2020). A purely hyperbolic discontinuous Galerkin approach for self- gravitating gas dynamics. Technical Report.

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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.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Schlottke-Lakemper, Michael mschlott@math.uni-koeln.de UNSPECIFIED UNSPECIFIED Winters, Andrew R. andrew.ross.winters@liu.se UNSPECIFIED UNSPECIFIED Gassner, Gregor J. ggassner@math.uni-koeln.de UNSPECIFIED UNSPECIFIED Ranocha, Hendrik UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-121976
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2020,6
Date:	1 October 2020
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language iscontinuous Galerkin spectral element method English multi-physics simulation English adaptive mesh refinement English compressible Euler equations English hyperbolic self-gravity English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/12197