Numerical solution of steady Navier-Stokes problems using integral representations

Steady-state incompressible Navier-Stokes and continuity equations are recast into integral representations for the velocity and the vorticity vector using the concept of fundamental solutions. Integrals are discretized using finite Fourier series approximations. An efficient iterative procedure is established for the numerical solution of internal flow problems in two dimensions. The iteration loop in this procedure is composed of a kinetic step and a kinematic step. Explicit computations are utilized in each step. Boundary vorticity values required for the kinetic step are determined from constraint equations obtained from the kinematic aspect of the problem expressed in the integral representation form. Several flow problems are studied numerically for various Reynolds numbers. Flow structures are determined from numerical results obtained. A Bachelor's flow model of constant vorticity is verified numerically for high Reynolds number closed streamline flows inside a circle.