Evaluation of Hypersingular Integrals Arising from Supersonic Flow Computations Using Higher Order Boundary Element Formulation

摘要

A general formulation is presented for evaluation of hypersingular integrals arising from computation of supersonic potential flows using boundary element method,where the element is partially inside the Mach forecone.The formulation is applied to higher order elements for any type of element intersection by the Mach forecone.General mappings are introduced to transform the inside-part of the elements partially inside the Mach forecone to another rectangular elements and analytical relations are derived for evaluation of the hypersingular integrals.Comparison between the results and exact solutions indicates that the method is not only general,but also is very accurate.