Implementation of linear and non-linear elastic biphasic porous media problems into FEATFLOW and comparison with PANDAS

Abstract

This dissertation presents a fully implicit, monolithic finite element solution scheme to effectively solve the governing set of differential algebraic equations of incompressible poroelastodynamics. Thereby, a two-dimensional, biphasic, saturated porous medium model with intrinsically coupled and incompressible solid and fluid constituents is considered. Our schemes are based on some well-accepted CFD techniques, originally developed for the efficient simulation of incompressible flow problems, and characterized by the following aspects: (1) a special treatment of the algebraically coupled volume balance equation leading to a reduced form of the boundary conditions; (2) usage of a higher-order accurate mixed LBBstable finite element pair with piecewise discontinuous pressure for the spatial discretization; (3) application of the fully implicit 2nd-order Crank-Nicolson scheme for the time discretization; (4) use of a special fast multigrid solver of Vanka-type smoother available in FEATFLOW to solve the resulting discrete linear equation system. Furthermore, a new adaptive time stepping scheme combined with Picard iteration method is introduced to solve a non-linear elastic problem with special hyper-elastic model. For the purpose of validation and to expose themerits and benefits of our new solution strategies in comparison to other established approaches, canonical one- and two-dimensional wave propagation problems are solved and a large-scale, dynamic soil-structure interaction problem serves to reveal the efficiency of the special multigrid solver and to evaluate its performance for different formulations.