A fast Riemann solver with constant covolume applied to the random choice method.

*(English)*Zbl 0673.76090Summary: The Riemann problem for the unsteady one-dimensional Euler equations together with the constant-covolume equation of state is solved exactly. The solution is then applied to the random choice method to solve the general initial-boundary value problem for the Euler equations. The iterative procedure to find \(p^*\), the pressure between the acoustic waves, involves a single algebraic (nonlinear) equation, all other quantities follow directly throughout the x-t plane, except within rarefaction fans where an extra iterative procedure is required. The solution is validated against existing exact results both directly and in conjunction with the random choice method.

##### Keywords:

Riemann problem; unsteady one-dimensional Euler equations; constant- covolume equation of state; random choice method; initial-boundary value problem; Euler equations
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\textit{E. F. Toro}, Int. J. Numer. Methods Fluids 9, No. 9, 1145--1164 (1989; Zbl 0673.76090)

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