A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media

作者：Radu Florin Adrian^*; Nordbotten Jan Martin; Pop Iuliu Sorin; Kumar Kundan

来源：Journal of Computational and Applied Mathematics, 2015, 289: 134-141.

DOI：10.1016/j.cam.2015.02.051

• Two-phase flow
• Linearization schemes
• Finite volume
• MPFA
• Convergence analysis

In this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite volumes have been used (more precisely the multi-point flux approximation method) and in time the backward Euler method has been employed. We present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization. We show that the scheme is linearly convergent. Numerical experiments are presented that sustain the theoretical results.

• 出版日期2015-12-1