FINITE-DIFFERENCE SOLUTIONS OF CONVECTION-DIFFUSION PROBLEMS IN IRREGULAR DOMAINS, USING A NONORTHOGONAL COORDINATE TRANSFORMATION

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Abstract
A solution methodology has been developed for convection-diffusion problems in which one boundary of the solution domain does not lie along a coordinate line. A nonorthogonal, algebraic coordinate transformation is used which yields a rectangular solution domain. This transformation avoids the task of numerically generating boundary-fitted coordinates. The discretized conservation equations are derived on a control-volume basis. These equations contain pseudodiffusion terms that result from the nonorthogonal nature of the transformation. The entire discretization procedure is documented in detail. Although it is not an essential feature of the method, the discretized equations and their solutions are tied in with the well-documented practices of the Patankar solution scheme for orthogonal systems. Application of the methodology is illustrated by two numerical examples.