Numerical Simulation of Two-Phase Porous Medium Flow with an Active Additive

The accuracy of the CABARET scheme (of second order) is compared with the accuracy of the WENO5 and A-WENO schemes (of fifth order in space and fourth order in time) as applied to the computation of various Riemann problems for a nonconvex system of conservation laws describing two-phase porous medium flow with an active additive. It is shown that CABARET is much more accurate than the WENO schemes, especially in exact-solution domains where centered rarefaction waves adjoin shock waves.