Comparison of Two Vortex-in-cell Schemes Implemented to a Three-dimensional Temporal Mixing Layer

Abstract

Numerical simulations are presented for three dimensional viscous incompressible free shear flows. The numerical method is based on solving the vorticity equation using Vortex-In-Cell method. In this method, the vorticity field is discretized into a finite set of Lagrangian elements (particles) and the computational domain is covered by Eulerian mesh. Velocity field is computed on the mesh by solving Poisson equation. The solution proceeds in time by advecting the particles with the flow. Second order Adam-Bashford method is used for time integration. Exchange of information between Lagrangian particles and Eulerian grid is carried out using the M’4 interpolation scheme. The classical inviscid scheme is enhanced to account for stretching and viscous effects. For that matter, two schemes are used. The first one used periodic remeshing of the vortex particles along with fourth order finite difference approximation for the partial derivatives of the stretching and viscous terms. In the second scheme, derivatives are approximated by least squares polynomial. The novelty of this work is signified by using the moving least squares technique within the framework of the Vortex-in-Cell method and implementing it to a three dimensional temporal mixing layer. Comparisons of the mean flow and velocity statistics are made with experimental studies. The results confirm the validity of the present schemes. Both schemes also demonstrate capability to qualitatively capture significant flow scales, and allow gaining physical insight as to the development of instabilities and the formation of three dimensional vortex structures. The two schemes show acceptable low numerical diffusion as well.