Navier-Stokes Equation using Discrete Del Operator and High-Speed Calculation of Poisson Equation

The finite-element method is universally applicable to fluid flow analysis in complex geometries. In finite element analysis, ordinary iterative methods of solving the Poisson equation repuire large amounts of computation time to satisfy the equation of continuity. In order to reduce the computation time, reduction of iteration in the Poisson equation is required. Increase of iteration occurs particularly when using an irregular mesh and in the analysis of three-dimensional problem. In this paper, we apply a modified weighting area method for GSMAC iteration and examine a new method for high speed calculation of the Poisson equation. The Navier-Stokes equation is written in rotational form using only a mass matrix and discrete del operator as the element coefficient matrices in order to reduce memory storage in the computer. The lid-driven cavity flow problem is chosen to verify the validity of the present numerical method.