Body-Fitted Coordinate Transformation for Finite Difference Method

Derivation process of the conservation equations from physical space to computational one for finite difference method was studied in this paper, and the opinion was given that the discrete identical equations were not true. According to the theoretical study and formula derivation, It was put forward that homogeneous governing equations which are widely used in CFD in body-fitted coordinates were just the approximation of those in Cartesian coordinates, and a source term should be introduced to balance the discrete equations. The source term was studied by numerical experiments, and the conclusion validates that the discrete source term is not always equal to 0 and has greater influence on numerical results compared with truncation errors. A consistency standard and a coupled algorithm were proposed about source term discretization on the basis of characteristics of mesh metrics and convective term, and the following numerical test proves that discretization errors can be eliminated completely in uniform cases.