The 2-dimensional Riemann problem for a 2 × 2 Hyperbolic conservation law II. Anisotropic media

We construct the solutions to a two-dimensional (2-D) Riemann problem for a 2 × 2 hyperbolic nonlinear system which models polymer flooding in an anisotropic oil reservoir. The construction demonstrates the importance of the shock, rarefaction, and contact "base points" and "base curves" in the determination of the solutions for 2-D Riemann problems. In particular, we establish some new relations between these. While specific details of the base points and curves are applicable only to this model, the existence of the curves and the existence of relationships between these curves are general features to be exploited for any hyperbolic system.