Abstract
AbstractThe aim of this paper is a derivation of a new multidimensional high‐resolution finite volume evolution Galerkin method for system of the Euler equations of gas dynamics. Instead of solving one‐dimensional Riemann problems in directions normal to cell interfaces the finite volume evolution Galerkin schemes are based on a genuinely multidimensional approach. The approximate solution at cell interfaces is computed by means of an approximate evolution operator taking all of the infinitely many bicharacteristics explicitly into account. Integrals along the Mach cones are evaluated exactly or by means of numerical quadratures. Second‐order resolution is obtained with a conservative piecewise bilinear recovery and the second‐order midpoint rule for the time integration. A numerical experiment which illustrates the good multidimensional approximation as well as higher‐order resolution is presented. Copyright © 2002 John Wiley & Sons, Ltd.
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