A stabilized sequential coupling algorithm for hydro-mechanical systems using reproducing kernel particle method

Sequential coupling scheme is a flexible numerical scheme to solve a coupled hydro-mechanical system. However, it suffers from severe numerical instability. Stability analysis of a sequential coupling scheme is performed in this paper. It is derived that the numerical scheme can be unconditionally stable with a stabilization term introduced to the fluid equation, while it is only conditionally stable without the stabilization. Reproducing Kernel Particle Method (RKPM) is used for spatial discretization. One dimensional consolidation in an elastic medium is conducted to verify the sequential scheme, and the convergence behavior during the iterations is presented.