A closed form for low order panel methods - D'elia, Jorge (2000)
A closed form for the computation of the dipolar and monopolar influence coefficients related to a low order panel method is shown. The flow problem is formulated by means of a three-dimensional potential model and the method of discretization is based in the Morino formulation for the perturbation velocity potential. On the  body surface this representation reduces to an integral equation with the source (or monopolar) and the doublet (or dipolar) densities. The first is found by application of the boundary condition, and the second is the unknown over the surface of the body. A lower panel method is used for the analytic integrations of the monopolar and dipolar influence coefficients with special attention to avoid a logarithmic singularity in the monopolar matrix when flat fairly structured meshes are used, common in ship-wave calculations.