Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006aspc..359..213r&link_type=abstract
Numerical Modeling of Space Plasma Flows: Astronum-2006 ASP Conference Series, Volume 359, Proceedings of the Conference Held 26
Astronomy and Astrophysics
Astronomy
Scientific paper
Residual distribution (RD) schemes, first introduced in the 1980's, are a promising class of numerical methods for solving hyperbolic conservation laws in complex geometries. Recent efforts have seen the development of high-order variants for smooth steady flows and high-resolution shock-capturing variants for time-dependent flows. In this work we modify the RD scheme of Abgrall and Mezine [J. Comput. Phys. 195 (2004) 474--507] so that it can be applied to hyperbolic balance laws in generalized coordinates. As a test case for this method, the shallow water equations are solved on a rotating sphere. This test case requires an additional modification to the RD scheme in order to to handle coordinate singularities at the north and south poles; in particular, the modification chosen to handle this issue is to solve the shallow water equations in standard latitude-longitude coordinates on most of the sphere, but to use different (non-singular) coordinates in the regions near the poles. This work is a first step towards developing accurate RD schemes for general relativistic hydrodynamics.
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