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

Michael Schlottke-Lakemper, Andrew R. Winters, Hendrik Ranocha, Gregor J. Gassner

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)110467
JournalJournal of Computational Physics
StatePublished - May 25 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-07-08
Acknowledgements: Michael Schlottke-Lakemper thanks Stefanie Walch for valuable insights on the application and performance of astrophysical simulation methods. Andrew Winters thanks Johannes Markert for helpful discussions on gravitational solvers and astrophysical applications. Gregor Gassner thanks the European Research Council for funding through the ERC Starting Grant “An Exascale aware and Un-crashable Space-Time-Adaptive Discontinuous Spectral Element Solver for Non-Linear Conservation Laws” (Extreme, grant no. 714487). Andrew Winters was supported by Vetenskapsrådet, Sweden award number 2020-03642 VR. Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications


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