Flow simulation around 3D bodies by using Lagrangian vortex loops method with boundary condition satisfaction with respect to tangential velocity components

Abstract

Abstract A new approach is developed for incompressible 3D flow simulation around bodies by Lagrangian vortex method. Closed vortex loops are considered as vortex elements, which are generated on all the body surface and provide the satisfaction of the boundary condition on the body surface. The procedure of the double layer potential density reconstruction, called T-scheme is proposed, which consists of two steps. Firstly, the integral equation with respect to vortex sheet intensity is solved, which expresses the equality between the tangential components of flow velocity limit value and the body surface velocity. It is solved by using Galerkin approach. Secondly, the least-squares procedure is implemented, which permits to find nodal values of the double layer potential density. It is shown that the developed algorithm makes it possible to improve significantly the quality of solution for the complex-shaped bodies with low-quality surface meshes. The combination of this approach with vortex wake modeling with vortex loops permits to simulate unsteady flows with acceptable computational complexity. It can be useful for CFD applications and visual effects reproducing in computer graphics.