Smoothed surface gradients for panel methods

Abstract

A weak form to computate the dipolar and monopolar surface gradients, related to a low order panel method, is shown. The flow problem is formulated by means of a three-dimensional potential model and the discretization is based on Morino´s formulation for the perturbation velocity potential. On the body surface this representation reduces to a boundary integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The first of them is found by application of the boundary flow condition, and the second one is the unknown over the body surface. A lower panel method is used for the analytic integrations of both the monopolar and dipolar influence coefficients. The surface velocity field is computed after solving the linear system, with a strong and a weak form of the Stokes theorem, which is oriented to fairly non-structured panel meshes. The proposed method is validated by comparing the numerical results with analytical ones for an isolated sphere and includes a prediction over a car-like configuration.