Prediction of laminar flow over a backward-facing step using a hybrid Eulerian-Lagrangian discrete vortex model

This paper describes a two-dimensional discrete vortex model for simulating low Reynolds number flows behind a backward-facing step. The numerical model employs a novel operator-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.