A Stabilization Procedure for Soil-water Coupled Problems Using the Mesh-free Method

The development of stability problems related to classical mixed methods has recently been observed. In this study, a soil-water coupled boundary-value problem, one type of stability problem, is presented using the Element-free Galerkin Method (EFG Method). In this soil-water coupled problem, anomalous behavior appears in the pressure field unless stabilization techniques are used. The remedy to such numerical instability has generally been to adopt a higher interpolation order for the displacements than for the pore pressure. As an alternative, however, an added stabilization term is incorporated into the equilibrium equation. The advantages of this stabilization procedure are as follows: (1) The interpolation order for the pore pressure is the same as that for the displacements. Therefore, the interpolation functions in the pore pressure field do not reduce the accuracy of the numerical results. (2) The stabilization term consists of first derivatives. The first derivatives of the interpolation functions for the EFG Method are smooth, and therefore, the solutions for pore pressure are accurate.In order to validate the above stabilization technique, some numerical results are given. It can be seen from the results that a good convergence is obtained with this stabilization term.