APSARA: A multi-dimensional unsplit fourth-order explicit Eulerian hydrodynamics code for arbitrary curvilinear grids

Abstract

We present a new fourth-order, finite-volume hydrodynamics code named Apsara. The code employs a high-order, finite-volume method for mapped coordinates with extensions for nonlinear hyperbolic conservation laws. Apsara can handle arbitrary structured curvilinear meshes in three spatial dimensions. The code has successfully passed several hydrodynamic test problems, including the advection of a Gaussian density profile and a nonlinear vortex and the propagation of linear acoustic waves. For these test problems, Apsara produces fourth-order accurate results in case of smooth grid mappings. The order of accuracy is reduced to first-order when using the nonsmooth circular grid mapping. When applying the high-order method to simulations of low-Mach number flows, for example, the Gresho vortex and the Taylor-Green vortex, we discover that Apsara delivers superior results to codes based on the dimensionally split, piecewise parabolic method (PPM) widely used in astrophysics. Hence, Apsara is a suitable tool for simulating highly subsonic flows in astrophysics. In the first astrophysical application, we perform implicit large eddy simulations (ILES) of anisotropic turbulence in the context of core collapse supernova (CCSN) and obtain results similar to those previously reported.

16 pages, 9 figures, 8 tables; accepted by Astronomy & Astrophysics

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• Hydrodynamics of core-collapse supernovae and their progenitors
• Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections
• An FFT-based Solution Method for the Poisson Equation on 3D Spherical Polar Grids
• A Proper Discretization of Hydrodynamic Equations in the Cylindrical Coordinates for Astrophysical Simulations
• WENO-Wombat: Scalable Fifth-Order Constrained-Transport Magnetohydrodynamics for Astrophysical Applications
• Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows
• Spectral Difference method with a posteriori limiting: II- Application to low Mach number flows
• A Generalized Solution Method for Parallelized Computation of the Three-dimensional Gravitational Potential on a Multi-patch grid in Spherical Geometry