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Paper: Residual Distribution Schemes for Hyperbolic Balance Laws in Generalized Coordinates
Volume: 359, Numerical Modeling of Space Plasma Flows: Astronum-2006
Page: 213
Authors: Rossmanith, J.A.
Abstract: 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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