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Curvilinear grids for WENO methods in astrophysical simulations. (English) Zbl 1360.85001

Summary: We investigate the applicability of curvilinear grids in the context of astrophysical simulations and WENO schemes. With the non-smooth mapping functions from D. A. Calhoun et al. [SIAM Rev. 50, No. 4, 723–752 (2008; Zbl 1155.65061)], 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.

MSC:

85-08 Computational methods for problems pertaining to astronomy and astrophysics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 1155.65061

Software:

ANTARES
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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