The solutions of the Riemann problem for a hyperbolic system modeling polymer flooding with hysteresis
The author derives a model describing two phase flow with hysteresis in porous media, in which the phases consist of water containing a dissolved polymer, and oil. For a constant concentration of polymer, the model reduces to a Buckley-Leverett equation with hysteresis. In the general case, the model consists of a nonstrictly hyperbolic system of three conservation laws concerning the saturation of water, the concentration of polymer and the hysteresis parameter -- denoted by \(\pi\) -- with a double-valued flux function, the branches of which are called primary and secondary. The author then distinguishes between six wave families, which are either stationary waves, primary or secondary Buckley-Leverett waves, primary, secondary, or \(\pi-\)field contact discontinuities. By means of these waves, he solves the Riemann problem in all possible cases.
scientific article; zbMATH DE number 1005580