InterPore2025

Finite volume methods for poromechanics

21 May 2025, 12:50

15m

Oral Presentation (MS12) Advances in computational and experimental poromechanics MS12

Speaker

Jan Martin Nordbotten (University of Bergen)

Description

In this talk, we survey recent advances in finite-volume type discretizations for mechanics and poromechanics. We will in particular discuss three classes of discretizations. 1) Multi-point stress finite volume methods (MPSA). 2) Two-point stress finite volume methods (TPSA). 3) Multi-point stress mixed finite element methods (MSMFE).

Being finite volume methods, the three classes of methods mentioned provide numerical approximations that have explicit flux and stress expressions, and where these fluxes and stresses balance exactly with the right-hand side of the equations. However, their different construction leads to both qualitative and quantitative differences.

We will provide a brief overview of the philosophy between each class of methods, and systematically address their strengths and weaknesses. Our qualitative discussion will emphasizing the generality of the methods in terms of grids, non-linearities, generalizability, and robustness in terms of degenerate parameters that are relevant in applications.

We will also survey more quantitatively the relative performance of the methods on a set of test cases.