Discretization Of Three Dimensional Non-Uniform Grid: Conditional Moment Closure Elliptic Equation Using Finite Difference Method

In most of the engineering problem, the solution meshing grid is non-uniform where it is in fine grid at the sensitive area of the simulation and coarse grid at the normal area. This is to ensure the simulation is accurate and utilizes appropriate resources. The discretization of non-uniform grid was done using Taylor expansion series and Finite Difference Method (FDM). Central method was used to minimize the error on the effect of truncation. The purpose of discretization is to transform the calculus problem (as continuous equation) to numerical form (as discrete equation). The steps are discretizing the continuous physical domain to discrete finite different grid and then approximate the individual partial derivative in the partial differential equation. This discretization method was used to discritize the CMC equation. The discrete form of CMC equation can be then coded using FORTRAN or MATLAB software.

Keywords: finite difference method, Taylor series, conditional moment closure, non-uniform grid, FORTRAN, MATLAB

M.M.Noor