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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.