Generalized finite volume framework for coupled consolidation and groundwater movement problems of poromechanics

In this paper, a generalized Finite Volume based numerical model, namely satBiotFoam is developed for simulating coupled consolidation and groundwater movement in fully saturated domain. The Biot Model equations are solved for fluid-saturated porous media and the model is developed over the open-source framework of OpenFOAM (R). The model equations pose a challenge numerically as they are inherently ill- conditioned and lead to instability. An iterative coupling approach is incorporated utilizing fixed-stress operator splitting with flexibility of tuning the coupling parameter. A modification in the theoretical coupling parameter is presented and studied for optimizing computational effort. Co-located grid systems of variables are prone to suffer from non-physical oscillations. A new Pressure-Implicit Splitting of Operators (PISO) based algorithm is presented capable of avoiding pressure oscillations. A generalized treatment of standard boundary conditions is presented to simulate a variety of poromechanics problems. An adaptive and stabilized time-stepping algorithm is incorporated in the model to speedup or slow down the simulation processes in order to ensure better convergence with least computational effort. A set of poromechanics problems are simulated for both the homogeneous and heterogeneous domains over structured or unstructured FV grid systems to establish the applicability of presented framework. The numerical results obtained from the model are oscillation-free and validated with the existing literature. satBiotFoam is capable of capturing non-monotonic pressure dissipation such as the Mandel-Cryer effect, observed in Mandel's 2-D Slab and Cryer's 3-D Sphere problems. The model has also been tested for groundwater withdrawal in a three-dimensional domain to capture the Noordbergum effect, seen in the adjacent non-pumping aquitards for the initial stages of pumping. Anew formulation is also presented to evaluate the mass conserving nature of the numerical model for simulated cases. A generalized approach with stable and accurate solutions establishes a foundation for further developments to simulate complex poromechanics problems.