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

Abstract

A higher-order method is developed that models continuous source and doublet singularity distributions over three-dimensional curved surfaces.  The singular on-surface influence coefficients are treated by a robust desingularisation algorithm, whereas off-surface coefficients are calculated by means of an efficient subdivision and variable cubature scheme.  Whilst higher-order methods have previously been developed for thick bodies and Dirichlet boundary conditions, this method is also capable of modelling continuous geometry and singularity surfaces over thin bodies and wakes that require Neumann boundary conditions. 

The Continuous Surface Method (CSM) has a number of advantages over conventional constant panel methods (CPMs).  Firstly, as curved geometries are represented exactly, changing the order of the solution does not modify the physical shape of the configuration.  Furthermore, as singularity solutions are continuous, the significant grid-dependency of CPMs does not arise.  Finally, the continuous singularity distributions allow velocities to be evaluated accurately across the entire surface without interpolation: this enables the calculation of continuous pressure distributions and the construction of streamlines and wakes flowing very close to surfaces, without any problems of divergence.

Numerical results comparing the CSM to a CPM have shown that for equal run times, the CSM obtains greater accuracy in pressure distributions that CPM, and produces much smoother velocity fields. However the CSM was not able to improve upon the efficiency of the CPM in determining total aerodynamic forces.

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