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Approximation of the genuinely multidimensional Riemann problem for the Euler equations by a Roe type method. I: The linearisation. (Approximation du problème de Riemann vraiment multidimensionnel des équations d’Euler par une méthode de type Roe. I: La linéarisation.) (French. Abridged English version) Zbl 0813.76074
Summary: We are interested in the approximation of the genuinely multidimensional Riemann problem for the Euler equations by a Roe type method. Here, the linearization problem only is studied; the resolution of the approximated Riemann problem is done in part II [see the following entry]. One starts by deriving a jump relation that generalizes the Rankine-Hugoniot ones. We show that the linearization problem generally has solutions; we define a criterion that enables to choose the right one. We end this note by a discussion on the validity of the Roe-Struijs-Deconinck’s linearization.

MSC:
 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 76L05 Shock waves and blast waves in fluid mechanics 35Q35 PDEs in connection with fluid mechanics