Nonlinear finite volume discretization of geomechanical problem

S. R. T. Tripuraneni, Aleksei Novikov, Denis Voskov*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

Elliptic differential operators describe a wide range of processes in mechanics relevant to geo-energy applications. Extensively used in reservoir modeling, the Finite Volume Method with TPFA can be consistently applied to discretize only a specific type of application under severe assumptions. In this paper, we introduce a positivity preserving Nonlinear Two Point Stress Approximation (NTPSA) based on the recently developed collocated Finite Volume scheme for linear elastic mechanics. The gradient reconstruction is different from the one used in Nonlinear TPFA, but a similar form of weighting scheme is employed to reconstruct the traction vector at each interface. The convergence of the scheme is tested with a homogeneous anisotropic stiffness tensor. The motivation behind the implementation of a new discretization framework in mechanics is to develop a uniform discretization technique preserving monotonicity for generic poromechanics applications.

Original languageEnglish
Pages (from-to)2283-2303
Number of pages21
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Volume47
Issue number12
DOIs
Publication statusPublished - 2023

Keywords

  • elasticity
  • homogenization function
  • nonlinear finite volume method
  • nonlinear two-point approximation

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