Abstract
In this paper, Free Mesh Method (a kind of meshless method) proposed by the authors is improved for application to steady incompressible viscous flow analysis. In the finite-element analysis of incompressible viscous flow, it is better to use different-order interpolation function for velocity and pressure. In the method, quadratic interpolation function can be used by introducing medium nodes between two original nodes, and a set of advection, diffusion and gradient matrices can be assembled independently node-by-node. As a numerical example, a two-dimensional driven cavity flow is analyzed. In this example, the governing equations, i.e. a coupled system of incompressibility and Navier-Stokes equations, are solved simultaneously. To solve a set of linear equations derived from the formulation of this method, the conjugate residual (CR) method is used. It is concluded that the result obtained using the method agrees well with the numerical result obtained by Ghia et al.
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