Article ID Journal Published Year Pages File Type
4615191 Journal of Mathematical Analysis and Applications 2015 21 Pages PDF
Abstract

In this study, we consider the two-dimensional Riemann problem for a system of conservation laws, which models polymer flooding in an anisotropic oil reservoir. The initial data are constants in three sectors centered at the origin, which only involve three contact discontinuities. By the generalized characteristic analysis method and the phase plane analysis method, we find that the solutions are not unique for certain values of the initial data. We propose an additional stability condition for the interaction of the contact discontinuities. By this stability condition, all of the exact solutions and their corresponding criteria can be obtained. The solutions exhibit various geometrical structures. In particular, envelope rarefaction waves develop in some solutions.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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