Mathematical model

The computational algorithm is based upon a consistent incremental formulation in the Eulerian framework, such that the incremental formulation uses the updated Lagrangian approach. The formulation is based on a quasi­static perturbation of the medium described by the Biot model which is constituted by poroelastic coefficients and the permeability governing the Darcy flow. The equilibrium equation and the mass conservation are expressed in the spatial, deformed configuration. Using the material derivative with respect to a convection velocity field, a rate formulation is derived which allows to approximate the residuum function associated with the unknown configuration using the last known configuration. The time­space discretization is based on an implicit time­integration scheme and conforming finite element approximation. A multistep approach uses a combination of the forward and backward finite differences. As an option, the Newmark integration scheme can be selected. The theoretical background and numerical tests have been published in:

Eduard Rohan, Vladimír Lukeš, Modeling large­deforming fluid­saturated porous media using an Eulerian incremental formulation, In Advances in Engineering Software, 2016, DOI:10.1016/j.advengsoft.2016.11.003, arXiv:1610.05103.