A Naturally Stabilized Semi-Lagrangian Meshfree Formulation for Multiphase Porous Media with Application to Landslide Modeling

Abstract

A stabilized meshfree formulation for modeling nonlinear, multiphase porous media with application to landslide simulation is presented. To effectively capture the hydromechanical couplings between solid and fluid phases, an efficient equal-order approximation pair is adopted in conjunction with the fluid pressure projection in the mixed formulation, which avoids spurious pressure oscillations caused by the violation of the inf-sup condition. Although semi-Lagrangian meshfree methods are well-suited for modeling extremely large deformation phenomena, their performance is severely impacted by improper domain integration techniques. In this work, the naturally stabilized nodal integration (NSNI) technique is employed to achieve a stable and efficient reproducing kernel mixed formulation. By using the implicit gradient approximation, the gradients of strain and fluid flux fields are added into the mixed formulation to eliminate spurious low-energy modes of nodal integration. This procedure adds little computational effort to the overall analysis. In addition, a set of modified test functions is introduced to ensure the variational consistency in the Galerkin formulation for multiphase porous media. The convergence, stability, and effectiveness of the semi-Lagrangian meshfree formulation are examined and demonstrated in several numerical examples, including the post-failure modeling of a partially saturated levee.