An unequal-order radial interpolation meshless method for Biot's consolidation theory

Abstract

Due to its second-order accuracy and unconditional stability, the Crank-Nicholson scheme is widely used to obtain numerical solutions of Biot's consolidation theory. However, spurious oscillation may occur when interpolations have equal orders for displacement and pore water pressure. This spurious oscillation may substantially degrade numerical accuracy. In order to avoid or alleviate spurious oscillation and improve numerical accuracy, a radial point interpolation meshless technique is proposed, with a polynomial for displacement that is one-order higher than for pore pressure. Three examples are numerically investigated with this meshless technique: a typical Terzaghi consolidation problem, a 2D consolidation problem, and a multi-layer consolidation problem. The numerical results are compared with the closed-form solution, the equal-order radial point interpolation method or FEM. The effects of the parameters of the current meshless method on spurious oscillation are studied. It is found that such an interpolation has consistent derivatives for both displacement and pore water pressure in an equilibrium equation. Spurious oscillation can thus be alleviated or even avoided, leading to high accuracy. © 2006 Elsevier Ltd. All rights reserved.