Topological Tools in the Solution of a Quadratic System of Two Conservation Laws
摘要
We utilize a three-dimensional manifold to solve Riemann problems for a system of two conservation laws with quadratic flux functions that exhibits an elliptic region in state-space. Points in this manifold represent potential shock waves, hence its name Wave Manifold. We calculate and graphically display the significant surfaces within in this manifold. We also construct shock, rarefaction, and composite curves, combine them to form wave curves, and intersect wave curves with surfaces to solve Riemann problems. We illustrate this algorithm with an example.