Incorporation and test of diffusion and strain effects in the two- dimensional vortex blob technique
Vorticity diffusion as well as small scale strain effects in a rotational fluid layer are incorporated in the vortex blob technique by changing the blob size. While the strain effect is computed by approximating the derivative of the normal velocity component across the layer, the vorticity diffusion is accounted for on the basis of the similarity solution for a diffusively spreading vortex sheet. This approach, which presents an alternative to the random walk method, allows us to track vorticity fronts in flows that do not conserve circulation such as miscible multiphase Hele-Shaw flows. We test the numerical method by comparing numerically obtained linear growth rates for an inviscid parallel shear layer and a miscible displacement process in a porous medium to exact results obtained from linear stability theory. When compared to the constant size vortex blob technique, the present extensions yield greatly improved results for the inviscid shear layer. For the diffusively spreading rotational layer arising in the miscible displacement process, the numerically obtained time-dependent growth rates show good quantitative agreement with exact results.
scientific article; zbMATH DE number 4089126
scientific article