Numerical simulation of laminar flow behind a backward-facing step using a viscous-splitting vortex algorithm

摘要

This paper describes a two-dimensional discrete vortex model for simulating the Navier-Stokes equations at low Reynolds numbers. The numerical model employs a novel form of 'viscous-splitting' technique to solve the vorticity-transport equation governing the evolution of vorticity. During the advective stage of the computation, a semi-Lagrangian scheme is used to update the vortex positions, whilst an analytical diffusion algorithm employing Oseen vortices is implemented during the diffusive time step. Redistributing the vorticity analytically instead of using the more traditional random-walk diffusion method enables the model to simulate steady flows directly, and avoids the need to filter the numerical results to remove the effects of the random walks. Predictions from the model are compared against experimental data of laminar flow past a backward-facing step at Reynolds numbers between 73 and 229. The results indicate the feasibility of the proposed discrete vortex scheme.