Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis

Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure

Algorithm development

The past decade has seen considerable activity in algorithm development for the Navier-Stokes equations. This has resulted in a wide variety of useful new techniques. Some examples for the numerical solution of the Navier-Stokes equations are presented, divided into two parts. One is devoted to the incompressible Navier-Stokes equations, and the other to the compressible form

Nonlifting wing-body combinations with certain geometric restraints having minimum wave drag at low supersonic speeds

Several variational problems involving optimum wing and body combinations having minimum wave drag for different kinds of geometrical restraints are analyzed. Particular attention is paid to the effect on the wave drag of shortening the fuselage and, for slender axially symmetric bodies, the effect of fixing the fuselage diameter at several points or even of fixing whole portions of its shape

Numerical Prediction Methods (Reynolds-Averaged Navier-Stokes Simulations of Transonic Separated Flows)

During the past five years, numerous pioneering archival publications have appeared that have presented computer solutions of the mass-weighted, time-averaged Navier-Stokes equations for transonic problems pertinent to the aircraft industry. These solutions have been pathfinders of developments that could evolve into a major new technological capability, namely the computational Navier-Stokes technology, for the aircraft industry. So far these simulations have demonstrated that computational techniques, and computer capabilities have advanced to the point where it is possible to solve forms of the Navier-Stokes equations for transonic research problems. At present there are two major shortcomings of the technology: limited computer speed and memory, and difficulties in turbulence modelling and in computation of complex three-dimensional geometries. These limitations and difficulties are the pacing items of the continuing developments, although the one item that will most likely turn out to be the most crucial to the progress of this technology is turbulence modelling. The objective of this presentation is to discuss the state of the art of this technology and suggest possible future areas of research. We now discuss some of the flow conditions for which the Navier-Stokes equations appear to be required. On an airfoil there are four different types of interaction of a shock wave with a boundary layer: (1) shock-boundary-layer interaction with no separation, (2) shock-induced turbulent separation with immediate reattachment (we refer to this as a shock-induced separation bubble), (3) shock-induced turbulent separation without reattachment, and (4) shock-induced separation bubble with trailing edge separation