After a brief introduction to hyperbolic conservation laws, we visit several models of polymer flooding in oil recovery. A special common feature shared by the models, i.e., the thermo-dynamics is decoupled from the hydro-dynamics, leads to a scalar conservation law with discontinuous flux. We discuss solution of Riemann problems as the vanishing viscosity limit. In particular, we show by counter examples that there exists infinitely many vanishing viscosity solution as one varies the ratio of the two viscosity parameters. Adding two monotonicity conditions, all double limits converge to the same function. We will also visit a related model for three component gas flooding, and present numerical solutions with front tracking.
Wen Shen is Professor at Mathematics Department of the Pennsylvania State University. Her research interests are nonlinear partial differential equations, their applications and numerical computation, especially hyperbolic conservation laws, relaxation model differential games, granular matter, and reservoir simulation.