InterPore2018 New Orleans

Novel finite-volume methods for anisotropic linear elasticity and poromechanics problems with full tensors

15 May 2018, 09:32

15m

New Orleans

Oral 20 Minutes MS 2.10: Advanced finite-volume methods for flow and transport in porous media Parallel 3-G

Speaker

Prof. Hamdi Tchelepi (Stanford University)

Description

We propose a novel finite volume method for anisotropic linear elasticity problem. The derivation of the flux approximation method for elasticity problem closely follows our previous work [1] on the nonlinear finite volume methods for diffusion equation featuring positivity and discrete maximum principles. It is based on the extensions of the harmonic point idea of [2] from the scalar to vector equations. We further extend the idea to coupled anisotropic flow and mechanics, featuring full tensors for permeability, Biot coefficient and stiffness tensor. Both methods handle star-shaped polyhedral grids, admit the construction of nonlinear finite volume methods and yield several new research directions.

[1] "Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem”, KM Terekhov, BT Mallison, HA Tchelepi // Journal of Computational Physics 330, 245-267
[2] "A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media.”, L Agelas, Rt Eymard, and R Herbin // Comptes Rendus Mathematique, 347. 11-12 (2009): 673-676.