Explicit Forms of the Fundamental Solution Tensor and Singular Integrals for the 2D Primitive-Variables Navier-Stokes Formulation

Abstract

This paper details the development of the explicit forms of the fundamental solutions for the two-dimensional incompressible unsteady time-difference primitive-variable Navier-Stokes boundary element formulation based on the method of Tosaka. Also, explicit forms of singular integrals are derived and presented. In this regard, series expansions of the fundamental solutions, which contain modified Bessel functions, are performed to enable integration of the singular cases. An algorithm for incorporating the singular solutions in to partitions of the affected boundary elements and domain cells is presented. Practical comments are offered in order to allow this method to be more readily used.