Parallel Discrete Vortex Methods on Commodity Supercomputers; an Investigation into Bluff Body Far Wake Behaviour

Parallel discrete vortex methods are ideally suited for studying the behaviour of bluff body wakes due to their ability to capture the motion of vortex structures and lack of downstream grid boundaries. However, the availability of suitable parallel computers to run long simulations is always an issue. The convergence of the high-end workstation and commodity PC markets means that it is now possible to build cheap, powerful supercomputer-level machines at a fraction of the cost of proprietary systems. The characteristics, programming methodology and performance of such systems is discussed in this paper. We also present results showing vortex merging behaviour in the far-wake of a circular cylinder. Previous simulations using the random walk method have shown a doubling of the shedding wavelength in the far wake compared with the near wake. New results using a deterministic vortex method are presented. The parallel vortex method used incorporates an O(NlogN) fast multipole method and vortex panel method to satisfy solid body boundary conditions. In order to account for viscous effects, both near the body and in the far wake, the vorticity redistribution method is used. This is considerably more accurate than stochastic methods and does not suffer from the regridding restrictions of the Particle Strength Exchange method. The aim of this paper is twofold. To present our findings on the behaviour of fully viscous, far wakes behind bluff bodies and to demonstrate that sufficient resource can be obtained on a cost-effective commodity supercomputer. Introduction The Discrete Vortex Method (DVM) is a technique that uses a Lagrangian framework to solve the Euler and Navier-Stokes Equations, circumventing many of the problems of grid-based methods. In this work, we use DVM's for simulating incompressible, homogenous, two-dimensional Newtonian fluid flow past bluff bodies. The main flow parameter is the vorticity of the fluid, defined as the curl of the local fluid velocity [1]. In the DVM, fluid velocity and pressure are regarded as a consequence of the solution rather than driving factors. The overall vorticity field is broken down into a number of computational elements that represent localised areas of fluid. In two dimensions these discrete vortices, also known as vortex blobs, induce a velocity on each other and are allowed to move with the fluid [1]. The vorticity, velocity and pressure fields can be calculated as a post-processing step rather than being inherently tied to the flow computation. 1 Viscous vortex method The incompressible, Navier-Stokes equations describing fluid flow are usually written in pressure-velocity form. However, it is perhaps more natural to look at the curl of the velocity field, resulting in the vorticity form of the Navier-Stokes equations (in two dimensions), ω ν ω ∂ ∂ω 2 . . ∇ = ∇ + u t (1)