Finite element method for coupled dynamic flow-deformation simulation

This article compares a solid velocity - liquid velocity formulation and a solid velocity - liquid pressure formulation for solving the coupled flow and deformation problem in an elastic media. The finite element formulations presented here apply to small deformations, but are in the process of being extended to large deformations within a material point formulation. As the material point model uses low-order elements and forward integration in time, the finite element model has to be composed accordingly. Dynamic simulations presented in this paper focus on capturing the first compression wave, which loads the liquid phase and solid phase, and on resolving the second compression wave, which starts the consolidation process. Whereas the velocity - velocity formulation properly captures two-phase dynamic behavior including the second wave, the velocity - pressure formulation is not capable of capturing the second compression wave. With regards to implementation within a material point framework, the first formulation is more consistent in the treatment of the solid and liquid phases, providing a physically based mapping of momentum for both phases, and is preferred for this reason.