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A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-05-25 , DOI: 10.1016/j.jcp.2021.110467
Michael Schlottke-Lakemper , Andrew R. Winters , Hendrik Ranocha , Gregor J. Gassner

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.



中文翻译:

用于自重气体动力学的纯双曲不连续Galerkin方法

用自重模拟天体物理流时的挑战之一是计算引力。与双曲流体力学方程相反,重力场由椭圆泊松方程描述。我们通过将椭圆问题重新构造为双曲扩散问题来提出纯双曲方法,该伪问题在伪时间中得以解决,使用与流动解决方案相同的显式高阶不连续Galerkin方法。流和重力解算器在联合的分层笛卡尔网格上运行,并通过源项双向耦合。我们方法的主要优点是,它可以不修改而重用现有的显式双曲求解器,同时保留其高级功能,例如不合格网格和可自适应求解的网格。通过更新流体力学求解器每个Runge-Kutta阶段的重力场,即使在耦合多物理场模拟中也可以实现高阶收敛。在验证了单物理场和多物理场设置的预期收敛顺序之后,我们通过对Jeans重力不稳定性的仿真来验证我们的方法。此外,我们通过计算自引力的Sedov爆炸,并在流求解器中捕获冲击并为整个耦合系统进行自适应网格细化,来证明我们的数值框架的全部功能。我们通过模拟Jeans重力失稳来验证我们的方法。此外,我们通过计算自引力的Sedov爆炸,并在流求解器中捕获冲击并为整个耦合系统进行自适应网格细化,来证明我们的数值框架的全部功能。我们通过模拟Jeans重力失稳来验证我们的方法。此外,我们通过计算自引力的Sedov爆炸,并在流求解器中捕获冲击并为整个耦合系统进行自适应网格细化,来证明我们的数值框架的全部功能。

更新日期:2021-05-25
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