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A multidimensional generalization of Roe’s flux difference splitter for the Euler equations. (English) Zbl 0790.76054
Flux difference splitting scheme for the one-dimensional Euler equations is presented as residual distribution scheme. Three steps are formulated when constructing upwind scheme. They are wave decomposition, conservative linearisation and scalar upwind distribution. This strategy is generalized to multidimensional case in which simple wave solutions serve as the basis of an eigenvector decomposition of the flux divergence. Conservative linearisation is performed assuming piecewise linear variation of the primary variables in triangles, the unknowns being defined at the vertices. Computational examples are presented which illustrate the performance of the scheme when using triangular meshes.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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