A projection method for porous media simulation*

Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. When fluid motion is approximated as incompressible, pressure in the pores acts as a Lagrange multiplier to satisfy the resulting constraint on fluid divergence. The resulting system of equations has no explicit representation of the pressure's time-evolution, which makes it difficult to solve numerically. In this talk, we present a method for the simulation of flow through porous media and its coupled elastic deformation that avoids this difficulty. The pore pressure field is calculated at each time step by correcting flow violation of the incompressibility condition in a manner similar to the Chorin projection method for incompressible fluid flow. The corresponding linear system over the pressure space has a number of favorable properties that make it easy to solve. In this talk, we will introduce the method and demonstrate its application to two- and three-dimensional systems arising in gel, mixture, and poroelastic theory.