On vortex sheet intensity reconstruction in meshless vortex particle method for two-dimensional flows simulation

Abstract

The problem of numerical solution of the boundary integral equation arising in 2D Lagrangian meshless vortex particle methods is considered. The Viscous vortex domains method used for viscous flow simulation, that leads to a large number of vortex particles in the flow domain, especially in the near-wall region. From a mathematical point of view, it leads, in turn, to the fast oscillating right-hand side of the integral equation. An original correction technique is developed that permits one to obtain a numerical solution with high resolution without grid refining. It is based on the Galerkin approach where additional terms are included in numerical solution expansion, that correspond to the subgrid-scale of the solution variation.