Numerical solutions of the two-dimensional averaged Navier-Stokes equations for the prediction of laminar, transitional, and turbulent flow fields around finite bodies of arbitrary shapes have been considered. Numerically generated body-fitted curvilinear coordinates and the relevant metric terms are used to provide the finite-difference solutions of the Navier-Stokes and the equations of turbulent quantities. Complete flow fields, including the boundary layer parameters, are obtained by using the zero, one and two-equations models for Schubauer's elliptical section, NACA663-018 airfoil, and a circular cylinder at free stream Reynolds numbers of 159,000, 1.2 and 1.4 million per foot respectively. In addition, a two-equation model with an algebraic-stress closure has also been developed. (Author).

A numerical solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations, which is implicit in time as well as space, has been developed for the case of a uniform flow past a body with rectangular boundaries undergoing pitch oscillations. The Navier-Stokes equations are written in the form of the vorticity equation and the Poisson equation for the stream function, thus using the vorticity and stream function as dependent variables, rather than the velocity components and the pressure. The equations are written in a moving coordinate system fixed with respect to the oscillating body, which undergoes pitch oscillations about an arbitrary axis. (Author).

This book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.