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

Abstract The paper investigates the system of PDEs for two-phase n -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 ) system into an n × 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.

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