A fast higher-order integral equation method for solution of the full potential equation around airfoils

A method based on an integral equation formulation is described for solution of the full potential equation in terms of the velocity field. In addition to the conventional distribution of singularities over the boundaries of field, a field source distribution is added in the flow region in order to represent the non-linear compressibility effect. The unknown source distribution in the field is calculated from the full potential equation by iteratively updating the normal velocity boundary conditions. In order to treat more complex configurations, local transformations provided by higher-order elements are used. Computation time required for integration of the domain is improved by using a domain decomposition. Results of calculations demonstrate substantial improvement in computation time and are in good agreement with independent results.