Salt cavern simulations with a stabilized mixed finite element formulation for low-order tetrahedral elements

Salt cavern simulations involve many numerical challenges that need to be addressed in order to ensure accurate and meaningful results. Firstly, lithological structures and solution-mined salt caverns always present fairly complex shapes, which favors the use of tetrahedral meshes with local refinements for adequate domain discretization. Secondly, salt rocks are known to creep under deviatoric stresses, meaning that deformations take place at constant volume (isochoric). The combination of isochoric deformations with tetrahedral meshes is particularly problematic for low-order finite element formulations. This work presents a stabilized mixed finite element (FE) formulation for linear tetrahedrons, where the mean stress is a primary variable, incorporating all the relevant deformation mechanisms for salt rocks. The stabilization consists of enriching the displacement FE approximation in the mean stress equation by obtaining an approximation for the Laplacian of the displacement that accounts for inelastic strains. This is achieved by using the Physical Influence Scheme (PIS) with the concept of secant Young’s modulus, which promotes local stabilizations where necessary. When combined with a proper calculation of a geometric parameter h, this stabilization technique is shown to produce oscillation-free and physically consistent results without any sort of tuning parameter. The proposed technique is analyzed in relevant test cases for salt cavern simulations and the results show the effectiveness of the proposed stabilization to eliminate spurious numerical oscillations with low-order tetrahedral meshes.