On a New Approach to 3D Meshless Flows Simulation Around Bluff Bodies by Using Vortex Method - Marchevsky, Ilia K.; Shcheglov, Georgy A. (Proceedings of the Conference Algoritmy, 2016)
The original approach is suggested for vortex sheet intensity computation when 3D flow around bluff bodies is being simulated using meshless Lagrangian vortex methods. Integral equation approximate solution is based on its approximation by the system of linear algebraic equations, which coefficients are expressed through improper integrals. In order to compute these integrals the numerical scheme is developed which allows to exclude the singularities, i.e., to split the integrals into regular and singular parts. Regular parts can be integrated numerically with high precision by using Gaussian quadrature formulae and for singular parts exact analytical expressions are derived.   The developed approach allows to raise significantly the accuracy of vortex method. It is shown that the developed semi-analytical procedure of integrals computation is much more accurate in comparison with direct numerical integration. The test problem of flow simulation around the sphere is considered. The exact analytical solution is known for it, and the developed approach provides more accurate results in comparison with `classical' 3D vortex method, especially when non-uniform unstructured triangular meshes are used for bodies surface representation.