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ExactRiemannSolver

v14	v15
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7	7	Given the above properties of the Riemann problem, an algebraic expression can be derived which gives p in the central "star-region" (denoted by ''). The overall structure of the Riemann problem then is to solve this algebraic equation for p. Once p* is known, u* follows immediately. The remaining rho_L and rho_R follow from expressions valid for the specific L- or R- wave present.
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	9	Specifically, this means that the code will determine at every point (x,t), that point's relative position to the different waves present. Once the position is determined, the solution is given by analytic expressions for the following five possibilities: pre- or post- shock, ahead of rarefaction head, behind rarefaction tail, or within the rarefaction fan. The position of each sampling point (x,t) is determined by a characteristic speed in the grid given by s = dx/t, where dx is the distance from the initial discontinuity to the sampling point (x,t), and t is the simulation end time.
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9	11	The program thus will consist of 4 parts: 1. Code to find p* using an iterative process, 2. Comparing p* to p_L and p_R to identify the types of nonlinear waves present in the solution, 3. Find remaining quantities in star region, where u* is given by simple expression in Toro (eqn. 4.9), and wave-specific expressions give rho_L and rho_R.