Updated users' guide for TAWFIVE with multigrid

A program for the Transonic Analysis of a Wing and Fuselage with Interacted Viscous Effects (TAWFIVE) was improved by the incorporation of multigrid and a method to specify lift coefficient rather than angle-of-attack. A finite volume full potential multigrid method is used to model the outer inviscid flow field. First order viscous effects are modeled by a 3-D integral boundary layer method. Both turbulent and laminar boundary layers are treated. Wake thickness effects are modeled using a 2-D strip method. A brief discussion of the engineering aspects of the program is given. The input, output, and use of the program are covered in detail. Sample results are given showing the effects of boundary layer corrections and the capability of the lift specification method

Time-accurate Navier-Stokes calculations with multigrid acceleration

A numerical scheme to solve the unsteady Navier-Stokes equations is described. The scheme is implemented by modifying the multigrid-multiblock version of the steady Navier-Stokes equations solver, TLNS3D. The scheme is fully implicit in time and uses TLNS3D to iteratively invert the equations at each physical time step. The design objective of the scheme is unconditional stability (at least for first- and second-order discretizations of the physical time derivatives). With unconditional stability, the choice of the time step is based on the physical phenomena to be resolved rather than limited by numerical stability which is especially important for high Reynolds number viscous flows, where the spatial variation of grid cell size can be as much as six orders of magnitude. An analysis of the iterative procedure and the implementation of this procedure in TLNS3D are discussed. Numerical results are presented to show both the capabilities of the scheme and its speed up relative to the use of global minimum time stepping. Reductions in computational times of an order of magnitude are demonstrated

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

The Sixth Copper Mountain Conference on Multigrid Methods was held on April 4-9, 1993, at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth

Design and analysis of low boom concepts at Langley Research Center

The objective of the sonic boom research in the current High Speed Research Program is to ultimately make possible overland supersonic flight by a high speed civil transport. To accomplish this objective, it is felt that results in four areas must demonstrate that such a vehicle would be acceptable by the general public, by the airframers, and by the airlines. It should be demonstrated: (1) that some waveform shape has the possibility of being acceptable to the general public; (2) that the atmosphere would not totally destroy such a waveform during propagation; (3) that a viable airplane could be built which produces such a waveform; and (4) that any performance penalty suffered by a low boom aircraft would be counteracted by the economic benefit of overland supersonic flight. The work being done at LaRC is in support of the third element listed above--the area of configuration design. The initial part of the paper will give a review of the theory being used for configuration designs and discuss two theory validation models which were built and tested within the past two years. Discussion of the wind tunnel and theoretical results (linear theory and higher order methods) and their implications for future designs will be included

Comparison of Jet Plume Shape Predictions and Plume Influence on Sonic Boom Signature

An Euler shock- tting marching code yields good agreement with semiempirically determined plume shapes, although the agreement decreases somewhat with increasing nozzle angle and the attendant increase in the nonisentropic nature of the ow. Some calculations for a low-boom con guration with a sample engine indicated that, for ight at altitudes above 60 000 ft, the plume e ect is dominant. This negates the advantages of a low-boom design. At lower altitudes, plume e ects are signi cant but of the order that can be incorporated into the low-boom design process

Behavior of plane relaxation methods as multigrid smoothers

Abstract. This paper contains the first published numerical results and analysis of the behavior of alternating plane relaxation methods as multigrid smoothers for cell-centered grids. The results are very satisfactory: plane smoothers work well in general and their performance improves considerably for strong anisotropies in the right direction because they effectively become exact solvers. In fact, the convergence rate decreases (improves) linearly with increasing anisotropy strength. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, the smoothing factor and cost per cycle of the different methods in the presence of strong anisotropies for Dirichlet boundary conditions are compared. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary; in fact, a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. As a result, alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems