Fast solvers and efficient numerical cfd techniques for dynamic porous media problems

We present a fully implicit, monolithic finite element solution scheme to efficiently solve the governing set of differential algebraic equations of incompressible poroelastodynamics. Thereby, we proceed from a two-dimensional, biphasic, saturated porous medium model with intrinsically coupled and incompressible solid and fluid constituents. Our approach, motivated by well-accepted CFD techniques and originally developed for the efficient simulation of incompressible flow problems, is 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 LBB-stable 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 for the resulting discrete linear equation system. For the purpose of validation and to expose the merits and benefits of our new solution strategy in comparison to other established approaches, canonical one- and two-dimensional wave propagation problems are solved. Finally, a large-scale, dynamic soil-structure interaction problem serves to reveal the efficiency of the special multigrid solver in combination with the chosen finite element discretization