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Numerical Treatment of State‐Dependent Permeability in Multiphysics Problems

Water resources research, 2023-08, Vol.59 (8), p.n/a [Peer Reviewed Journal]

2023 The Authors. ;2023. This article is published under http://creativecommons.org/licenses/by-nc/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;ISSN: 0043-1397 ;EISSN: 1944-7973 ;DOI: 10.1029/2023WR034686

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  • Title:
    Numerical Treatment of State‐Dependent Permeability in Multiphysics Problems
  • Author: Stefansson, Ivar ; Keilegavlen, Eirik
  • Subjects: Approximation ; Aquatic reptiles ; Convergence ; Darcy's law ; Darcys law ; Deformation ; Finite volume method ; finite volume methods ; Fluctuations ; Linearization ; multiphysics simulations ; Newton methods ; Newton's method ; nonlinear PDEs ; Nonlinear systems ; Nonlinearity ; Permeability ; Porous media ; Simulation models ; state‐dependent permeability
  • Is Part Of: Water resources research, 2023-08, Vol.59 (8), p.n/a
  • Description: Constitutive laws relating fluid potentials and fluxes in a nonlinear manner are common in several porous media applications, including biological and reactive flows, poromechanics, and fracture deformation. Compared to the standard, linear Darcy's law, such enhanced flux relations increase both the degree of nonlinearity, and, in the case of multiphysics simulations, coupling strength between processes. While incorporating the nonlinearities into simulation models is thus paramount for computational efficiency, correct linearization, as is needed for incorporation in Newton's method, is challenging from a practical perspective. The standard approach is therefore to ignore nonlinearities in the permeability during linearization. For finite volume methods, which are popular in porous media applications, complete linearization is feasible only for the simplest flux discretization, namely the two‐point flux approximation. We introduce an approximated linearization scheme for finite volume methods that is exact for the two‐point scheme and can be applied to more advanced and accurate discretizations, exemplified herein by a multi‐point flux stencil. We test the new method for both nonlinear porous media flow and several multiphysics simulations. Our results show that the new linearization consistently outperforms the standard approach. Moreover our scheme achieves asymptotic second order convergence of the Newton iterations, in contrast to the linear convergence obtained with the standard approach. Key Points State‐dependent permeability produces strong nonlinearity in multiphysics problems Ignoring state dependency in solution scheme severely impacts convergence A novel approach differentiating the finite volume flux stencil greatly improves nonlinear convergence
  • Publisher: Washington: Blackwell Publishing Ltd
  • Language: English
  • Identifier: ISSN: 0043-1397
    EISSN: 1944-7973
    DOI: 10.1029/2023WR034686
  • Source: Wiley Blackwell AGU Digital Archive
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