The least-squares meshfree method for the steady incompressible viscous flow

A least-squares meshfree method (LSMFM) based on the first-order velocity-pressure-vorticity formulation for two-dimensional steady incompressible viscous flow is presented. The discretization of all governing equations is implemented by the least-squares method. The equal-order moving least-squares (MLS) approximation is employed. Gauss quadrature is used in the background cells constructed by the quadtree algorithm and 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. A numerical example with analytical solution for the Stokes problem is devised to analyze the error estimates of the LSMFM. Also, cavity-driven flow for the Stokes problem and the flow past a circular cylinder at low Reynolds numbers for the steady incompressible viscous flow are solved. Through the comparisons of the LSMFM's results with other experimental and numerical results, the numerical features of the presented LSMFM are investigated and discussed.