A B-Spline Higher-Order Panel Method Applied to Two-Dimensional Lifting Problem

A higher-order panel method based on B-spline representation for both the geometry and the solution is developed for the solution of the flow around two-dimensional lifting bodies. The influence functions due to the normal dipole and the source are separated into the singular and nonsingular parts; then the former is integrated analytically, whereas the latter is integrated using Gaussian quadrature. Through a desingularization process, the accuracy of the present method can be increased without limit to any order by selecting a proper numerical quadrature. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting foils with far fewer panels than existing low-order panel methods.