Two finite element approaches for Darcy and Darcy–Brinkman flow through deformable porous media—Mixed method vs. NURBS based (isogeometric) continuity

Abstract Porous media problems with coupled finite deformations and flow are still quite challenging. If large deformations occur, a non homogeneous porosity field is almost inevitable, as the porosity can vary due to deformation or due to flow and pore pressure. From a numerical point of view this significantly changes the mathematical description of the problem. In this contribution, we will analyze the consequences of the occurrence of porosity gradients on the finite element formulations of saturated, two phase porous media for Darcy and Darcy–Brinkman flow. We will present two approaches which are capable of fulfilling the numerical requirements for convergence. The first will be an approach based on NURBS shape functions. The second is a mixed formulation including the porosity as primary solution field. In addition, we will propose a method to include no-penetration or no-slip constraints into the monolithic system using a dual Lagrange multiplier method. The potential of the proposed methods for solving porous flow structure interaction undergoing large deformations will be illustrated by numerical examples.

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