Research is proposed in the development of novel numerical algorithms for the solution of partial differential equations arising in computational fluid dynamics. Issues of interest include the use of novel adaptive grid techniques for compressible and incompressible flows in two and three dimensions, the inclusion of chemistry terms for combustion and hypersonic flow and the suitability of SIMD architectures, such as the Connection Machine, for any type of adaptive grid algorithms. Computer science techniques will be combined with the mathematics of numerical computations in carrying out the proposed research.
