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NASA NTRS1988

Patch structured surface grid with dynamic curvature clustering

The numerical technique developed by Eiseman (1985) to generate surface grids with lines clustered in areas of greater curvature is described and demonstrated. This approach combines the direct active use of surface curvature with a mean-value relaxation scheme and multigrid methods; it permits an arbitrary number of patches to be organized in a single integer array based on a patch number, an edge number, and a boundary-condition index. Grids for typical CFD applications are presented and briefly characterized.

Wang, YI↗

NASA NTRS1989

Advances in fluid dynamics

Various papers on advances in fluid dynamics are presented. Individual topics addressed include: nonunique solutions of the Euler equations; numerical solution of the biharmonic equation using a spectral multigrid method; finite-volume shape and placement for efficiency, accuracy, and physics; NND schemes and their application to numerical simulation of complex plume flow problems; symbolic analysis and computational algorithm construction; and velocity and mass flux distribution measurements of spherical glass beads in air flow in a 90-deg vertical-to-horizontal bend. Also discussed are: hyperbolic solution adaptive mesh generation; progress and future directions in CFD; numerical simulation of shock focusing; microbubble formation and splitting in a turbulent boundary layer for turbulence reduction; numerical study of spherical Taylor-Couette flow, trajectories of vortex lines beneath a free surface or above a plane; and a mathematical model for response of the coronary circulation to high sustained gravitational force fields.

Ballhaus, W. F., Jr.↗

NASA NTRS1990

Numerical analysis of secondary flow in a two-stage turbine

The three-dimensional viscous average passage flow in the Pratt and Whitney alternate design Space Shuttle Main Engine fuel turbine has been simulated. The effect of secondary flows generated by upstream blade rows on the performance of downstream blade rows is studied. The numerical results are compared to the design intent to validate improved models in the average passage equations. Analysis of the results centers on the primary spanwise mixing mechanism in this low aspect ratio turbine. A multigrid method has also been incorporated to improve the overall convergence rate of the numerical algorithm.

Kirtley, K. R.↗

NASA NTRS1990

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Bates, J. R.↗

NASA NTRS1990

Navier-Stokes analysis of transonic cascade flow

A new kind of C-type grid is proposed, this grid is non-periodic on the wake and allows minimum skewness for cascades with high turning and large camber. Reynolds-averaged Navier-Stokes equations are solved on this type of grid using a finite volume discretization and a full multigrid method which uses Runge-Kutta stepping as the driving scheme. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A detailed numerical study is proposed for a highly loaded transonic blade. A grid independence analysis is presented in terms of pressure distribution, exit flow angles, and loss coefficient. Comparison with experiments clearly demonstrates the capability of the proposed procedure.

Arnone, A.↗

NASA NTRS1991

Characteristics of 3D turbulent jets in crossflow

Three dimensional turbulent jets in crossflow at low to medium jet-to-crossflow velocity ratios are computed with a finite volume numerical procedure which utilizes a second-moment closure model to approximate the Reynolds stresses. A multigrid method is used to accelerate the convergence rate of the procedure. Comparison of the computations to measured data show good qualitative agreement. All trends are correctly predicted, though there is some uncertainty on the height of penetration of the jet. The evolution of the vorticity field is used to explore the jet-crossflow interaction.

Demuren, A. O.↗

NASA NTRS1991

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

Chen, H. C.↗

NASA NTRS1991

CFD in the 1980's from one point of view

The present interpretive treatment of the development history of CFD in the 1980s gives attention to advancements in such algorithmic techniques as flux Jacobian-based upwind differencing, total variation-diminishing and essentially nonoscillatory schemes, multigrid methods, unstructured grids, and nonrectangular structured grids. At the same time, computational turbulence research gave attention to turbulence modeling on the bases of increasingly powerful supercomputers and meticulously constructed databases. The major future developments in CFD will encompass such capabilities as structured and unstructured three-dimensional grids.

Lomax, Harvard↗

NASA NTRS1991

Diagonal implicit multigrid solution of compressible turbulent flows

The Caughey (1988) multigrid diagonal implicit algorithm for Euler equations is extended to solve the two-dimensional thin layer Navier-Stokes equations for turbulent transonic flows. To further accelerate convergence to a steady state, the implicit scheme is used within the multigrid method. Results are presented for transonic flows past airfoils, and the flow-field results are compared with other computational data and experiments demonstrating the accuracy of the method.

Varma, R. R.↗

NASA NTRS1991

Multigrid calculation of three-dimensional viscous cascade flows

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

NASA NTRS1990

Characteristics of 3D turbulent jets in crossflow

Demuren, A. O.↗

NASA NTRS1991

Multigrid calculation of three-dimensional viscous cascade flows

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Arnone, A.↗

NASA NTRS1992

Navier-Stokes solution of transonic cascade flows using nonperiodic C-type grids

Arnone, Andrea↗

NASA NTRS1992

Applications of multigrid software in the atmospheric sciences

Elliptic partial differential equations from different areas in the atmospheric sciences are efficiently and easily solved utilizing the multigrid software package named MUDPACK. It is demonstrated that the multigrid method is more efficient than other commonly employed techniques, such as Gaussian elimination and fixed-grid relaxation. The efficiency relative to other techniques, both in terms of storage requirement and computational time, increases quickly with grid size.

Adams, J.↗

NASA NTRS1993

Characteristics of three-dimensional turbulent jets in crossflow

Three-dimensional turbulent jets in crossflow at low to medium jet-to-crossflow velocity ratios are computed with a finite volume numerical procedure which utilizes a second-moment closure model to approximate the Reynolds stresses. A multigrid method is used to accelerate the convergence rate of the procedure. Comparison of the computations to measured data show good qualitative agreement. All trends are correctly predicted, though there is some uncertainty on the height of penetration of the jet. The evolution of the vorticity field is used to explore the jet-crossflow interaction.

Demuren, A. O.↗

NASA NTRS1993

A Navier-Stokes solver for turbomachinery applications

A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.

Arnone, A.↗

NASA NTRS1993

Implicit multigrid techniques for compressible flows

Recent advances in the development of the diagonalized alternating direction implicit multigrid method for compressible aerodynamic problems are reviewed. These include the extension of the method originally developed for the Euler equations to include viscous effects, the computation of turbulent flows and the implementation on parallel computers of the scheme on multiblock rids.

Caughey, David A.↗

NASA NTRS1991

A multiblock, multigrid solution procedure for multielement airfoils

A block-structured grid formulation is presented and discussed. The compressible Euler equations are solved on the decomposed domain with a multigrid method based on Runge-Kutta time stepping and centered spatial differencing. The flexibility of the multiblock approach is demonstrated by computing low speed inviscid flow over two different multielement airfoil configurations.

Sanetrik, Mark D.↗