Curvilinear Grids for WENO Methods in Astrophysical Simulations

TL;DR

This paper explores the use of curvilinear grids in astrophysical simulations with WENO schemes, demonstrating their advantages and challenges, and comparing finite difference and finite volume approaches for different flow regimes.

Contribution

It introduces the application of non-smooth curvilinear grids in WENO-based astrophysical simulations and discusses implementation challenges and solutions.

Findings

Finite volume WENO schemes perform well on non-smooth grids and low Mach flows.

Finite difference WENO schemes are limited to smooth, high Mach flows.

Curvilinear grids expand the scope of numerical astrophysics simulations.

Abstract

We investigate the applicability of curvilinear grids in the context of astrophysical simulations and WENO schemes. With the non-smooth mapping functions from Calhoun et al. (2008), we can tackle many astrophysical problems which were out of scope with the standard grids in numerical astrophysics. We describe the difficulties occurring when implementing curvilinear coordinates into our WENO code, and how we overcome them. We illustrate the theoretical results with numerical data. The WENO finite difference scheme works only for high Mach number flows and smooth mapping functions whereas the finite volume scheme gives accurate results even for low Mach number flows and on non-smooth grids.