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

A hybrid numerical scheme is presented to compute turbulent shear flows. The scheme divides the computational domain D into two regions, D sub 1 and D sub 2 and the vorticity equation is solved by different methods in each region. In region D sub 1, a Lagrangian formulation (vortex-in-cell) is used, while in region D sub 2 an Eulerian formulation (finite-difference) is used. At the boundary between the two regions, discrete Lagangian vorticity can be convected and converted into Eulerian grid vorticity. Conversely, Eulerian fluxes of vorticity at this boundary are discretized so that in D vorticity is conserved and vorticity transport does not realize the imposition of the artificial boundary. This particular method has been developed to compute spatially-developing turbulent shear layers in two dimensions. Turbulent shear layers have a large range of length scales from the initial thin boundary layer near the splitter plate to large coherent vortex structures which continue to grow with downstream distance. Thus, by starting with discrete Lagrangian vorticity and changing to continuous Eulerian vorticity, the advantages of both methods can be used to simulate a larger flowfield domain than achievable with either method alone.