A combined analytical singularity subtraction method and compact implicit differencing scheme for aerodynamic mixing

In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical. With this restriction, it may be concluded that an important family of methods for mathematical/computational development are reduced or approximate models. In this study, a combined perturbation/numerical modeling methodology is developed. The numerical portion of the model uses a compact finite difference scheme, while analytical solutions are used to resolve singular behavior that is inherent to this flow. Solutions are presented to illustrate the efficiency of this methodology.