|A method for the application of vorticity based potential-flow solvers to unstructured surface meshes has been created. This method is designed to maintain the advantages of the vorticity based solvers while removing the limitations of geometrical inputs associated with the philosophical approach. A discussion on the necessity and advantages of this approach has been presented. A modification to the evaluation of skin-friction coefficients using surface vorticity has also been developed. An unstructured wake-strand model has been developed to allow handling of wakes emanating from unstructured meshes. An attempt has been made to extend potential-flow solvers to the current industry surface meshing and numerical solver standards. A test-suite of basic shapes and bodies was tested to evaluate the fidelity of the new approach. An advanced test-suite was developed to stress-test the solver as well as to test out the geometry handling pipeline required to handle these test cases. It was determined that the solver is able to provide high fidelity results for a wide variety of test cases and is able to: work with conformal and non-conformal geometry interfaces, resolve surface intersections, work with both structured and unstructured meshes, work with both thick and thin bodies and work with manifold and non-manifold surface interfaces.