Abstract
The vorticity-vector potential formulation method is combined with the 4th-order accurate centered finite difference method without numerical dissipation. The flow in a square cavity is solved at large Reynolds numbers in order to verify effectivity of the computational method. This method is shown to be useful for solving the flow accurately with a small number of grid points as compared with the 2nd-order accurate method. The present method also resolves well the unsteady motion in a square cavity at the Reynolds number of l04. The dynamic subgrid scale turbulence model is implemented in the present computational method. The LES of transition to turbulence in a plane channel is carried out. It is shown that vortices initially roll up from the Tollmien-Schlichting waves, spike and tear, and finally form an array after complex vortical structure. The turbulence statistics are compared with the DNS and the experimental values, and considerable agreement is obtained.
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