Author(s): Jason P. Hughes; David I. Graham
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Keywords: SPH; Pressure Poisson equation; Boundary Conditions; Low Re
Abstract: This paper reports the results of incompressible smoothed particle hydrodynamics (ISPH) computations of very low Reynolds number lid-driven cavity flow. In this case, particles can be ‘ frozen ’ and the method can be viewed as a fixed grid method. I-SPH is a two-step predictor-corrector projection method. An explicit predictor integrates the contributions from viscous and body forces. An implicit corrector then updates the velocity by adding a curl-free contribution that is proportional to the pressure gradient. An intermediate step requires the solution of a pressure Poisson equation with boundary conditions of zero normal gradients on solid surfaces. Here, three different formulations are used to implement these conditions and the results compared and contrasted. A convergence study is carried out for each of the three boundary formulations and for two ratios of smoothing length to inter particle spacing (1, 1. 2). Results for 10x10, 17x17, 25x25, 35x35, 50x50, 75x75 and 100x100 particles are presented and the ‘ error’ characterised as a function of the inter-particle spacing. =dx h /
Year: 2007