Two-dimensional viscous flow computations on the Connection Machine: Unstructured meshes, upwind schemes and massively parallel computations. (English) Zbl 0767.76049

Summary: We report on 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.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
76M10 Finite element methods applied to problems in fluid mechanics
65Y05 Parallel numerical computation
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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