Pressure-displacement coupling in poroelasticity. further details of a stable finite volume formulation

This paper further explores fundamental issues on the behaviour of a finite volume technique using staggered grids for solving poroelasticity problems. Attention is given to the well-known drawback of pressure instabilities, which arises in certain conditions, as in low permeability media, fast transients and undrained conditions. Finite volume techniques are not the first choice for solving poroelasticity problems, and the reason is cultural, since finite elements have a successful history in solving solid mechanics problems. It has been demonstrated, however, that the finite volume strategies can be successfully applied to poroelasticity problems, with the advantage of offering a single method, stable, and fully conservative for both, fluid mass and forces balance

Efficient solvers for hybridized three-field mixed finite element coupled poromechanics

We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible conditions. The efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a Schur-complement approximation strategy. Robustness, computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures

A stabilized element-based finite volume method for poroelastic problems

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of different types. One of the difficulties for solving these equations is the numerical pressure instability that can arise when undrained conditions take place. In this paper, a stabilization technique is developed to overcome this problem by employing an interpolation function for displacements that considers also the pressure gradient effect. The interpolation function is obtained by the so-called Physical Influence Scheme (PIS), typically employed for solving incompressible fluid flows governed by the Navier\u2013Stokes equations. Classical problems with analytical solutions, as well as three-dimensional realistic cases are addressed. The results reveal that the proposed stabilization technique is able to eliminate the spurious pressure instabilities arising under undrained conditions at a low computational cost