A hybrid vortex-in-cell finite-difference method for shear layer computation

A hybrid numerical scheme is presented to compute turbulent shear flows. The equations of motion are assumed to be the vorticity and continuity equations and are to be solved in a given domain. The scheme divides the domain into two regions and uses a Lagrangian method in one region and an Eulerian method in the other. The two regions interact through the boundary separating them and the influence of the vorticity field in one region on the other region is accounted for by solving for the stream function in the entire domain. This scheme has been tested by simulating the interactions of two vortices in a square box. The solution obtained with this new method agrees with the solutions obtained using an Eulerian method, a vortex-in-cell method, and a grid-free vortex method. A two-dimensional mixing layer is simulated using this new method. Vortex formation and pairing are observed. The growth of the momentum thickness is found to be linear with the downstream distance. Self-similarity of the mean velocity and turbulence intensities profiles is observed. Comparison of these profiles with experimental data shows good agreement.