Variational Modeling of Porosity Waves

Mathematical models for finite-strain poroelasticity in an Eulerian formulation are studied by constructing their energy-variational structure, which gives rise to a class of saddle-point problems. This problem is discretized using an incremental time-stepping scheme and a mixed finite element approach, resulting in a monolithic, structure-preserving discretization. The Eulerian formulation is based on the inverse deformation, the so-called reference map. We present examples from geophysical applications, where elasticity and diffusive fluid flow are fully coupled and can be used to describe porosity waves, i.e., localized ascending fluid waves driven by gravitational forces.