On Mixed Isogeometric Analysis of Poroelasticity

Abstract

Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite element analyses. We present a mixed isogeometric formulation here with a view to assessing the results at very small time steps. Numerical studies are performed on Terzaghi's problem and consolidation of a layered porous medium with a very low permeability layer for varying polynomial degrees, continuities across knot spans and spatial discretizations. Comparisons are made with equal order simulations.

Optimal spectral approximation of2n-order differential operators by mixed isogeometric analysis

“…Again, most of the work in this area focuses on the fluid flow problems where various isogeometric formulations were applied to the Stokes problem [17,37,42,54]. Recent advances include mixed isogeometric formulations for elasticity [34] and poromechanics [13,32]. In this field, coupling the fluid pressure and the solid deformation, mixed isogeometric formulations violate the inf-sup condition and suffer from numerical instabilities in the incompressible and the nearly incompressible limit.…”