On Application of Body Conforming Curvilinear Grids for Finite Difference Solution of External Flow,

Finite difference practitioners frequently make use of arbitrary coordinate transforms and introduce body conforming curvilinear grid systems. The coordinate transforms may either be built globally in mappings from physical space to computational space, or they may be built in locally in the finite volume sense. The advantages of using body conforming curvilinear grids in finite difference flow field simulation include the following Body conforming grids simplify the application of boundary conditions insofar that grid lines will coincide with the body boundary. Curvilinear grids may be clustered to flow field action regions to improve solution accuracy. Body conforming grids may allow simplification of the governing equations. Such grids can also help maintain a well-ordered system of algebraic equations suitable for vector-computer processing or approximate-factorization-implicit techniques. The subject of this paper is not the generation of body conforming curvilinear grids rather it is the use of such grids in finite difference applications. In Section 2 of this paper the difficulties of solving the transformed equations in conservative form are discussed. In Section 3 various experiences are cited to suggest that considerable computational efficiency can yet be gleaned by further improvements of the grid. Concluding remarks follow in Section 4.