Boundary conditions for the weak formulation of the mixed (u,p) poroelasticity problem

Abstract

This paper presents the boundary conditions that apply to the weak integral formulation of the Biot mixed (u_,p) poroelasticity equations. These boundary conditions are derived from the classical boundary conditions of the Biot displacement (u_,U_) poroelasticity equations. They are applied to the surface integrals of the associated weak form to account for exterior excitations, supports, and couplings with exterior elastic, acoustic, poroelastic media, and a septum. It will be shown that the derived boundary conditions for the (u_,p) formulation lead to simpler finite element equations compared to those obtained from the (u_,U_) formulation. Finally, two numerical examples are presented to validate the poroelastic-septum coupling condition, and to highlight the limitations of the free edge condition on a poroelastic medium.