A modified Trefftz method for fluid flow

Steady 2D inviscid laminar flow is investigated numerically using a modified version of the method proposed by Trefftz (1926). An approximate solution based on fundamental solutions with singularities located outside the problem domain is employed, as in the regular-boundary-integral method of Patterson and Sheikh (1981). The technique developed is then applied to confined flow past a circular body, confined flow at normal incidence to a plate, and unconfined flow past an NACA airfoil. The results are presented in graphs and tables and compared to those obtained by a conventional boundary-element method or analytically. For a given discretization, both numerical methods produced good results on the interior but experienced degradation at the boundaries. While the convergences of the methods were similar, the present method requires less computation because no integrations are involved.