A higher-order potential flow method for thick bodies, thin surfaces and wakes

A higher-order panel method for analysing the three-dimensional potential flow fields around bodies and wakes is presented. The geometric surfaces are represented by continuous curved patches, with no discretization into panels. These geometric patches hold singularity distributions that have C2 continuity, and which are solved by applying Dirichlet or Neumann boundary conditions at discrete collocation points. While higher-order methods have previously been developed for thick bodies and Dirichlet boundary conditions, this potential flow method is capable of modelling continuous geometry and singularity surfaces over thin bodies and wakes. The continuous surface method has a number of advantages over conventional constant panel methods. Firstly, as curved geometries are represented exactly, changing the order of the solution does not modify the physical shape of the configuration under investigation. Furthermore, the continuous singularity distributions allow velocities to be evaluated accurately across the entire surface rather than just at collocation points. This means that pressure distributions can be calculated exactly without interpolation, and streamlines can be constructed very close to surfaces without problems of divergence. Finally, body and wake surfaces do not exhibit the strong modelling singularities that can present difficulties with wake relaxation. Copyright q 2007 John Wiley & Sons, Ltd