Sammendrag
We discuss the application of modern high-resolution schemes to a hyperbolic system that models polymer flooding. This system consists of a pair of non-strictly hyperbolic conservation laws. In general, high-resolution schemes are often used for model problems where high accuracy is required in the presence of shocks or discontinuities. Polymer flooding is a difficult process to model, especially since the dynamics of the flow lead to concentration fronts that are not self-sharpening. Because the water viscosity is strongly affected by the polymer concentration, it is crucial to capture polymer fronts accurately to resolve the nonlinear displacement mechanism correctly and its efficiency for enhanced recover. The main objective of this work is to compare different first- and higher-order methods in terms of how the discontinuities are treated. The discussion will focus on the validity, convergence and robustness of the schemes. Especially, different initial conditions and the inclusion of adsorption and permeability reduction can change not only the solution, but also the behavior of the different numerical methods. We show that these effects also can influence the applicability of a solver and we investigate of how suitable different numerical methods are for different polymer flooding situations.