A heterogeneous multiscale method for poroelasticity
In this thesis, we develop and analyze a heterogeneous multiscale model for coupled fluid flow and solid deformation in porous media based on operator splitting and finite volume method. The splitting method results in two elliptic multiscale PDE's in the form of a reaction diffusion equation and a linear elasticity equation. We extend our previous multiscale method from 1D to higher dimensions and develop new approaches for the inclusion of mixed boundary conditions and source terms. We derive an error estimate for our multiscale method and analyze the stability of our splitting method. We also test the effectiveness of our method in the case of steady state linear poroelasticity.
Applied Mathematics|Mechanical engineering
Delgado, Paul M, "A heterogeneous multiscale method for poroelasticity" (2015). ETD Collection for University of Texas, El Paso. AAI3708537.