ADAPTIVE GRID GENERATION BY ELLIPTIC EQUATIONS WITH GRID CONTROL AT ALL OF THE BOUNDARIES

Abstract

A method that combines Anderson's grid method and a grid-point control scheme is developed in order to solve elliptic equations in a manner that simultaneously controls grid spacing and orthogonality on all of the boundaries. Both the finite-difference and finite-volume methods have become increasingly important in the solving of partial differential equations. These numerical methods rely on discretization of the domain of definition, most frequently employing numerical grid generation. In order to accurately solve a problem numerically, the proper location of the nodal points of the computational domain and the orthogonal grid around the boundaries are of prime importance. While the adaptive grid method resolves physical variables by moving grid points from areas of small solution variation to regions of larger variation, it does not address problems associated with the gradient of a physical quantity normal to the boundaries. This latter factor is particularly important for friction factor or heat transfer coefficient evaluation. If orthogonality at the mesh points adjacent to the boundaries can be guaranteed, then the error induced from the treatment of the boundary conditions can be decreased. One of the most popular methods for grid generation involves solving the elliptical partial differential equation; however, the choice ofmore » control functions poses a major problem. The authors combine previous techniques in order to produce a grid generation system that gives the desired grid control over all the boundaries. The present investigation combines the adaptive grid procedure with their previously developed grid and boundary grid methods are first restated. Subsequently, several numerical tests will be employed to demonstrate the applicability of the proposed method.« less