Monotone nonlinear finite‐volume method for nonisothermal two‐phase two‐component flow in porous media. (12th December 2016)

• Record Type: Journal Article
• Authors: Schneider, Martin; Flemisch, Bernd; Helmig, Rainer
• Is Part Of: International journal for numerical methods in fluids. Volume 84:Number 6(2017)
• Page Start: 352
• Page End: 381
• Publication Date: 2016-12-12
• Subjects: finite‐volume -- monotone discretization -- multi‐point flux -- multi‐phase flow -- porous media -- nonlinear solvers; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4352
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: This article presents a new nonlinear finite‐volume scheme for the nonisothermal two‐phase two‐component flow equations in porous media. The face fluxes are approximated by a nonlinear two‐point flux approximation, where transmissibilities nonlinearly depend on primary variables. Thereby, we mainly follow the ideas proposed by Le Potier combined with a harmonic averaging point interpolation strategy for the approximation of arbitrary heterogeneous permeability fields on polygonal grids. The behavior of this interpolation strategy is analyzed, and its limitation for highly anisotropic permeability tensors is demonstrated. Moreover, the condition numbers of occurring matrices are compared with linear finite‐volume schemes. Additionally, the convergence behavior of iterative solvers is investigated. Finally, it is shown that the nonlinear scheme is more efficient than its linear counterpart. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : We present a new monotone nonlinear finite‐volume scheme for the nonisothermal two‐phase two‐component flow equations in porous media. The behavior of this scheme is analyzed, and the condition numbers of occurring matrices are compared with linear finite‐volume schemes. Additionally, the convergence behavior of iterative solvers is investigated, and it is shown that the nonlinear scheme is more efficient than its linear counterpart.