Wave Interactions for the Pressure Gradient Equations

In this paper, we solve the Riemann problem for a coupled hyperbolic system of conservation laws, which arises as an intermediate model in the flux splitting method for the computation of Euler equations in gasdynamics. We study the properties of solutions involving shock and rarefaction waves, and establish their existence and uniqueness. We present numerical examples for different initial data, and finally discuss all possible elementary wave interactions; it is noticed that in certain cases the resulting wave pattern after interaction is substantially different from that which arises in isentropic gasdynamics.

Keywords

Pressure-gradient equations, wave interactions, Riemann problem, shock, rarefaction wave

2010 Mathematics Subject Classification

35L60, 35L65, 76L05, 76N15

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Published 1 January 2010