NUMERICAL COMPUTATION OF DOUBLE SURFACE INTEGRALS OVER TRIANGULAR CELLS FOR VORTEX SHEET INTENSITY RECONSTRUCTION ON BODY SURFACE IN 3D VORTEX METHODS
Free (open access)
47 - 61
ILIA MARCHEVSKY, GEORGY SHCHEGLOV
In this paper, a new approach is developed for the computation of vortex sheet intensity in vortex methods for 3D flow simulation. The problem is reduced to a boundary integral equation of the second kind on the body surface with respect to an unknown vector variable. The proposed technique makes it possible to improve the accuracy significantly in comparison to the technique traditionally implemented in vortex methods. A Galerkin-type approach is used with piecewise-constant basis functions. The coefficients of the resulting algebraic system are expressed through double surface integrals, calculated over the mesh cells. A semi-analytic technique is developed for the integrals calculation; integration over one cell is carried out analytically, while at the integration over the other cell (having common edge or vertex with the first one), the integrand is singular. Analytic expressions are obtained for singular parts of integrands and for the results of their integration. The regular parts of the integrands are integrated numerically. The developed approach provides less than 0.1% error. The regularization technique is developed for a divergence-free vortex sheet reconstruction on the body surface. The developed approach works well on coarse and non-uniform surface meshes for complex-shaped bodies, which is important for engineering applications.
vortex methods, double layer potential, vortex sheet, boundary integral equation, singularity exclusion, numerical integration