Compact Accurately Boundary-Adjusting high-REsolution Technique for fluid dynamics

Authors:
S. A. Karabasov;V. M. Goloviznin
Affiliations:
Cambridge University, Engineering Department, Whittle Laboratory, 1J.J. Thompson Avenue, Cambridge CB3 0DY, United Kingdom;Mathematical Modelling Division, Moscow Institute of Nuclear Safety, 52B. Tulskaya, Moscow 113191, Russia
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

A novel high-resolution numerical method is presented for one-dimensional hyperbolic problems based on the extension of the original Upwind Leapfrog scheme to quasi-linear conservation laws. The method is second-order accurate on non-uniform grids in space and time, has a very small dispersion error and computational stencil defined within one space-time cell. For shock-capturing, the scheme is equipped with a conservative non-linear correction procedure which is directly based on the maximum principle. Plentiful numerical examples are provided for linear advection, quasi-linear scalar hyperbolic conservation laws and gas dynamics and comparisons with other computational methods in the literature are discussed.