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

• Florin Adrian Radu ^[1] ; Jan Martin Nordbotten ^[1] ; Iuliu Sorin Pop ^[1] ; Kundan Kumar ^[1]
  1. [1] University of Bergen

     University of Bergen

     Noruega

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 289, Nº 1 (1 December 2015), 2015, págs. 134-141
• Idioma: inglés
• DOI: 10.1016/j.cam.2015.02.051
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• Resumen

  • 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.