Least-squares meshfree method for incompressible Navier-Stokes problems

Abstract

A least-squares meshfree method based on the first-order velocity-pressure-vorticity formulation for two-dimensional incompressible Navier-Stokes problem is presented. The convective term is linearized by successive substitution or Newton's method. The discretization of all governing equations is implemented by the least-squares method. Equal-order moving least-squares approximation is employed with Gauss quadrature in the background cells. The boundary conditions are enforced by the penalty method. The matrix-free element-by-element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. Cavity flow for steady Navier-Stokes problem and the flow over a square obstacle for time-dependent Navier-Stokes problem are investigated for the presented least-squares meshfree method. The effects of inaccurate integration on the accuracy of the solution are investigated. Copyright (C) 2004 John Wiley Sons, Ltd.