Analysis of Numerical Errors of the Hess Smith Panel Method With Asymmetric Meshes

Although less accurate in comparison with most of the existing high-order panel methods, the Class Hess Smith panel method is still popular for potential flow calculations due to its simplicity, robustness, and especially efficiency. In the application where the method is adopted for the problems in concern, the method is usually first validated and analyzed for numerical accuracy prior to the application. This is a common practice as also seen in almost all the literature. However, the objects chosen for validation and accuracy analysis are often geometrically symmetric (most typically, spheres) and discretized into symmetric meshes. However, such analysis with symmetric meshes does not actually reveal the numerical errors as the body involved in the problem in concern or the flow around the body may not be symmetrical. In this paper, the numerical errors of the Hess Smith method are systematically analyzed with asymmetrical meshes. The values of various quantities associated with isolated panels and also the entire body are obtained and compared with the Hess Smith panel method does exhibit a very different error pattern.