A method for solving three-dimensional viscous incompressible flows over slender bodies

A marching iterative method for solving the three-dimensional incompressible and steady reduced Navier-Stokes equations in general orthogonal coordinate systems is described with the velocity and the pressure as dependent variables. The coupled set of the linearized finite-difference continuity and momentum equations are solved iteratively without any splitting or factorization errors. Each iteration consists of spatial marching from the upstream boundary to the downstream boundary. The discrete continuity and the two linearized crossflow momentum equations are satisfied at each marching step, even when the mainstream momentum equation is not converged. This solution procedure is equivalent to the solution of a single Poisson-like equation by the successive plane over relaxation method, while other available solution methods employ a Jacobi-type iterative scheme and therefore are less efficient. Several properties of the numerical method have been assessed through a series of tests performed on the laminar incompressible flow over prolate spheroids at intermediate incidence.