2-DIMENSIONAL VISCOUS-FLOW COMPUTATIONS ON THE CONNECTION MACHINE - UNSTRUCTURED MESHES, UPWIND SCHEMES AND MASSIVELY PARALLEL COMPUTATIONS

Here we report on our effort in simulating two-dimensional viscous flows on the Connection Machine, using a second-order accurate monotonic upwind scheme for conservation laws (MUSCL) on fully unstructured grids. The spatial approximation combines an upwind finite volume method for the discretization of the convective fluxes with a classical Galerkin finite element method for the discretization of the diffusive fluxes. The resulting semi-discrete equations are time integrated with a second-order low-storage explicit Runge-Kutta method. A communication efficient strategy for mapping thousands of processors onto an arbitrary mesh is presented and proposed as an alternative to the fast north-east-west-south (NEWS) communication mechanism, which is restricted to structured grids. Measured performance results for the simulation of low Reynolds number chaotic flows indicate that an 8K CM-2 (8192 processors) with single precision floating point arithmetic is at least as fast as one CRAY-2 processor.