On Mixed Isogeometric Analysis of Poroelasticity

TL;DR

This paper introduces a mixed isogeometric analysis approach for poroelasticity, addressing pressure oscillations at small time steps, and evaluates its effectiveness through numerical studies on classical problems.

Contribution

The paper presents a novel mixed isogeometric formulation for poroelasticity, specifically targeting pressure oscillation issues at small time steps, with comprehensive numerical validation.

Findings

Mixed isogeometric approach reduces pressure oscillations.

Higher polynomial degrees improve solution accuracy.

Comparison shows advantages over equal order simulations.

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.