Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies

A method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected region containing any number of arbitrarily shaped bodies is presented. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system. Numerical solutions for the lifting and nonlifting potential flow about Joukowski and Karman-Trefftz airfoils using this coordinate system generation show excellent comparison with the analytic solutions. The application to fields with multiple bodies is illustrated by a potential flow solution for multiple airfoils.