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South, J. C., Jr.

Publications and source records attributed to South, J. C., Jr..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Stability analysis of intermediate boundary conditions in approximate factorization schemes

The paper discusses the role of the intermediate boundary condition in the AF2 scheme used by Holst for simulation of the transonic full potential equation. It is shown that the treatment suggested by Holst led to a restriction on the time step and ways to overcome this restriction are suggested. The discussion is based on the theory developed by Gustafsson, Kreiss, and Sundstrom and also on the von Neumann method.

South, J. C., Jr.↗
NASA NTRS1986

Advances in numerical and applied mathematics

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

South, J. C., Jr.↗
NASA NTRS1985

Recent advances in computational transonic aerodynamics

The near-term prospects are discussed for calculation of viscous transonic flow fields about realistic configurations at full-scale Reynolds numbers. Three basic algorithms are considered: The central-difference, three-factor ADI method; the central-difference, explicit, multistep Runge-Kutta method with multigrid acceleration; and the relaxation method for the upwind-differenced, flux-split equations. Each method has distinct advantages and disadvantages regarding stability, convergence rate, and vectorizability. It appears that computation times can be 15 to 60 hours on the latest super computers unless 3D algorithms are improved to perform as well as current 2D algorithms.

South, J. C., Jr.↗
NASA NTRS1985

Finite-volume scheme for transonic potential flow about airfoils and bodies in an arbitrarily-shaped channel

A conservative finite-volume difference scheme is developed for the potential equation to solve transonic flow about airfoils and bodies in an arbitrary channel. The scheme employs a mesh which is a nearly-conformal 'O' mesh about the airfoil and nearly orthogonal at the channel walls. The mesh extends to infinity upstream and downstream, where the mapping is singular. Special procedures are required to treat the singularities at infinity, including computation of the metrics near those points. Channels with exit areas different from inlet areas are solved; a body with a sting mount is an example of such a case.

South, J. C., Jr.↗
NASA NTRS1984

Vectorized schemes for conical potential flow using the artificial density method

A method is developed to determine solutions to the full-potential equation for steady supersonic conical flow using the artificial density method. Various update schemes used generally for transonic potential solutions are investigated. The schemes are compared for speed and robustness. All versions of the computer code have been vectorized and are currently running on the CYBER-203 computer. The update schemes are vectorized, where possible, either fully (explicit schemes) or partially (implicit schemes). Since each version of the code differs only by the update scheme and elements other than the update scheme are completely vectorizable, comparisons of computational effort and convergence rate among schemes are a measure of the specific scheme's performance. Results are presented for circular and elliptical cones at angle of attack for subcritical and supercritical crossflows.

Bradley, P. F.↗
NASA NTRS1983

A method for solving the transonic full-potential equation for general configurations

A method is developed for solving the full-potential equation for two-dimensional and axisymmetric flow which retains the grid and boundary condition simplicity of the transonic small-disturbance codes. The method is based on a finite-volume formulation of the mass conservation equation in a Cartesian coordinate system, and is an extension of the method of Purvis and Burkhalter (1979). This finite-volume approach, combined with the simple boundary treatment, is shown to result in a highly robust method applicable to a wide range of geometries and flow conditions. The accuracy of the method is demonstrated for general geometries in two-dimensional and axisymmetric flows. The use of this method results in significant gains in convergence rate over the vertical-line over-relaxation scheme by incorporating an AF2-type algorithm (Ballhaus et al., 1978). It is suggested that the simplicity of this method shold allow a relatively easy extension to complex geometries in three-dimensional flows, and complex two-dimensional configurations such as multielement airfoils should be amenable to this method.

Wedan, B.↗
NASA NTRS1983

Stability analysis of intermediate boundary conditions in approximate factorization schemes

In many cases, approximate factorization schemes have provided a significant increase in efficiency over previously used solution methods in certain problems. The present investigation is concerned with the importance of intermediate boundary conditions in approximate factorization schemes, taking into account a specific example regarding a boundary-induced stability restriction in a scheme for the transonic full-potential equation. The considered scheme has been discussed by Holst (1979). Holst's scheme is a variation of the AF2 schemes described by Ballhaus and Steger (1975). The application of the AF2 scheme to the two-dimensional Laplace equation in a rectangle is studied giving attention to the stability of the scheme in connection with various boundary conditions for the intermediate variable.

South, J. C., Jr.↗
NASA NTRS1982

Transonic potential flow and coordinate generation for bodies in a wind tunnel

An accurate method has been developed for computation of transonic potential flow about a 2-D lifting airfoil or an axisymmetric body in a wind tunnel. The computational mesh is nearly orthogonal everywhere and is generated by a sequence of Schwarz-Christoffel transformations and shearings to obtain an '0' grid near the body. A conservative finite-volume scheme for the full-potential equation and exact boundary conditions is used together with 'retarded' density to solve efficiently transonic flow with embedded shocks and large regions of supersonic flow. Supersonic free-stream flows are also solved with captured bow shocks and embedded subsonic regions.

Doria, M. L.↗
NASA NTRS1981

Report of the panel on theoretical aerodynamics

Interactions between theoretical aerodynamics and the NTF are discussed. The development and validation of computational fluid dynamics computer codes, the determination of Reynolds number scaling laws, and extension of the data bases of entrainment type turbulence models to include high Reynolds number data are recommended areas of study. The major benefit theoretical aerodynamics could have on the NTF is in the quantitative description of wind tunnel wall interference effects.

South, J. C., Jr.↗
NASA NTRS1981

Conservative full-potential calculations for axisymmetric, transonic flow

A conservative, finite-difference, full-potential relaxation code has been developed to solve transonic flow around axisymmetric or nonlifting, planar, two-dimensional bodies. The program utilizes the artificial compressibility method to provide an upwind bias in supersonic regions. Calculated examples include a wide variety of axisymmetric and planar two-dimensional shapes with various blunt, pointed and open ends in subsonic, transonic, and low supersonic free streams. Comparisons between conservative and nonconservative full-potential calculations show perfect agreement at convergence when the flow is entirely subsonic. Noticeable differences exist, however, between the conservative and nonconservative solutions for transonic flows with shocks.

Green, L. L.↗
NASA NTRS1981

Inviscid transonic flow over axisymmetric bodies

Axisymmetric transonic flow is of interest not only because of its practical application to missile and launch vehicle aerodynamics but also because of its relation, in terms of area rule, to fully three dimensional flow. RAXBOD computer program analyzes steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses finite-difference relaxation method to solve numerically exact formulation of disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important.

South, J. C., Jr.↗
NASA NTRS1979

Vector processor algorithms for transonic flow calculations

This paper discusses a number of algorithms for solving the transonic full-potential equation in conservative form on a vector computer, such as the CDC STAR-100 or the CRAY-1. Recent research with the 'artificial density' method for transonics has led to development of some new iteration schemes which take advantage of vector-computer architecture without suffering significant loss of convergence rate. Several of these more promising schemes are described and 2-D and 3-D results are shown comparing the computational rates on the STAR and CRAY vector computers, and the CYBER-175 serial computer. Schemes included are: (1) Checkerboard SOR, (2) Checkerboard Leapfrog, (3) odd-even vertical line SOR, and (4) odd-even horizontal line SOR.

South, J. C., Jr.↗
NASA NTRS1977

Application of a multi-level grid method to transonic flow calculations

A multi-level grid method has been studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g., 8 x 2 mesh cells) to fine (e.g., 128 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with, say, optimal SLOR iterations on the finest grid. The method was applied to the solution of the transonic small-disturbance equation for the velocity potential in the conservation form. Nonlifting transonic flow past a parabolic-arc airfoil is the example studied, with meshes of both constant and variable step size.

South, J. C., Jr.↗
NASA NTRS1976

Influence of nonconservative differencing on transonic streamline shapes

A computer program recently developed by South and Brandt (1976) which contained the Murman (1973) conservative finite-difference scheme is easily modified to use the Garabedian and Korn (1971) nonconservative finite difference scheme. This program solves the transonic small disturbance equation for only symmetric flow, but incorporates several iterative solution techniques. Results are presented for the case where the equally spaced computational grid extended to infinity in both the streamwise and normal directions. Streamline shapes are obtained along several grid lines by a streamwise integration of the normal component of the perturbation velocity. Comparison cases are run for a 10% thick parabolic arc airfoil at zero incidence for freestream Mach numbers of 0, 0.70, 0.84, and 0.95. It is shown that the use of a nonconservative finite-difference scheme in transonic flow calculations destroys the global mass balance when shocks are present. This lack of mass balance may prove to be more crucial in the case of an unconfined external flow.

Newman, P. A.↗