Splitting in systems of PDEs for two-phase multicomponent flow in porous media

The paper investigates the system of PDEs for two-phase nn-component flow in porous media consisting of hyperbolic terms for advective transport, parabolic terms of dissipative effects and relaxation non-equilibrium equations. We found that for several dissipative and non-equilibrium systems, using the stream-function as a free variable instead of time separates the general (n+1)×(n+1)(n+1)×(n+1) system into an n×nn×n auxiliary system and one scalar lifting equation. In numerous cases, where the auxiliary system allows for exact solution, the general flow problem is reduced to numerical or semi-analytical solution of one lifting equation.