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Multidimensional schemes for nonlinear systems of hyperbolic conservation laws. (English) Zbl 0843.65064
Griffiths, D. F. (ed.) et al., Numerical analysis 1995. Proceedings of the 16th Dundee conference on numerical analysis, University of Dundee, UK, June 27-30, 1995. Harlow: Longman. Pitman Res. Notes Math. Ser. 344, 19-35 (1996).
We derive the decomposition of the Euler equations into infinitely many transport equations and give ways how to reduce these infinitely many equations to a finite number of equations. We show in one-space dimension how correction terms can be incorporated such as to create a second-order scheme. We describe the overall scheme and give numerical examples.
For the entire collection see [Zbl 0837.00017].

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76N15 Gas dynamics (general theory)