Two dimensional flow simulation using discrete vortex methods on MIMD processor arrays

Abstract

The discrete vortex method is a Lagrangian technique for solving the two-dimensional Navier- Stokes equations for an incompressible homogeneous Newtonian fluid. The construction of a robust numerical solver, based on the discrete vortex method, is discussed in detail. The viscous effects are modelled using both the random walk and diffusion velocity techniques. The computational cost is reduced by using a zonal decomposition algorithm for the velocity summation and by formulating an implementation suitable for execution on MIMD' parallel architecture computers. The code is validated using the problem of impulsively started flow past a circular cylinder at Reynolds numbers ranging from 300 to 31,700. Short/medium time solutions for both the rotating and non-rotating cases are used to confirm the accuracy of the method by comparison with experimental and numerical results from the literature. Long time solutions for the non- rotating case reveal non-determinism at high Reynolds numbers: the flows can exhibit a multiplicity of vortex shedding patterns. The low-speed stall process on NACA four-digit wing sections is visualised. A detailed comparison of the flow past a symmetric aerofoil with the flow past a cambered aerofoil shows that the camber delays the onset of the stall. Multiple Instruction Multiple Data

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