| A novel high-order panel method is developed for potential flows. These Uniform Bi-Cubic B-Spline (UBCBS) panels are intended for the simulation of unsteady, nonlinear, three-dimensional, free-surface waves. The integral-equation-based method is formulated using Green's theorem, with singular-kernel integrals which are evaluated numerically using a series of variable transformations to desingularize the kernels. The issue of edge conditions for surfaces defined by B-splines is addressed, and the edge conditions are integrated into the panel method. A novel implementation of the familiar Orlanski radiation conditions is developed specifically for use with these panels.;Unlike existing panel methods, UBCBS panels guarantee a continuous normal vector everywhere on the discretized free-surface. They are high-order, allowing representation of complex wave forms with relatively few grid points. Analytical expressions are presented for the spatial derivatives of the potential, allowing evaluation of the velocity vector at any point on the problem boundary, without finite differencing. Free-surface boundary conditions are imposed without the introduction of numerical damping, yet the computations appear stable.;Validation and convergence studies are conducted by comparing computed results with analytical solutions for several test cases, including the well-known Cauchy-Poisson wave elevation problem.;Computations are presented for the nonlinear Cauchy-Poisson problem and for the nonlinear waves generated by a translating submerged spheroid. The results provide a high level of detail using a relatively small number of gridpoints. Pressure is easily and accurately evaluated. Symmetric edge conditions are shown to be effective for modeling a plane of symmetry, and the radiation condition effectively suppresses spurious reflections at the open boundary. |
