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An asymptotic expansion for the solution of the generalized Riemann problem. II: Application to the equation of gas dynamics. (English) Zbl 0703.35106
[For part I, cf. the second and the third author, ibid. 5, No.2, 179-207 (1988; Zbl 0679.35064).]
This paper applies the general theory of approximation of generalized Riemann solutions due to the second and the third author to the equations of gas dynamics.
Explicit formulae are derived for the first order approximation of such solutions. This approximation allows to construct easily a second order accurate version of the numerical Godunov method.
Reviewer: A.Bourgeade

35L65 Hyperbolic conservation laws
35C20 Asymptotic expansions of solutions to PDEs
76N15 Gas dynamics (general theory)
35A35 Theoretical approximation in context of PDEs
35L67 Shocks and singularities for hyperbolic equations
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