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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Multi-grid solution of Neumann pressure problem for viscous flows using primitive variables

The multi-grid (MG) technique has been advanced for use with the Neumann boundary-value problem in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of viscous flows using the velocity-pressure formulation of the Navier-Stokes equations. With successive over-relaxation (SOR) as the smoothing operator and with suitably formulated restriction and coarse-grid-correction operators, a 4-grid procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 5, depending on the problem parameters. Thy influence of the smoothing operator is also examined by employing the alternating-direction implicit and the strongly implicit techniques instead of SOR.

Ghia, U.↗
NASA NTRS1992

Unstructured grid solutions to a wing/pylon/store configuration using VGRID3D/USM3D

The purpose of this paper is to validate an inviscid flow solution package based on a new unstructured grid methodology using experimental data on a wing/pylon/store configuration. The solution package consists of an advancing front unstructured grid generator, VGRID3D, and an efficient Euler equation solver, USM3D. Comparisons of computed data versus experimental data are made for two free-stream Mach numbers at five store locations relative to the wing. Both rigid body aerodynamics and mutual interference effects are explored. A very good agreement is observed between computed and wind tunnel data.

Parikh, Paresh↗
NASA NTRS2007

USM3D Unstructured Grid Solutions for CAWAPI at NASA LaRC

In support the Cranked Arrow Wing Aerodynamic Project International (CAWAPI) to improve the Technology Readiness Level of flow solvers by comparing results with measured F-16XL-1 flight data, NASA Langley employed the TetrUSS unstructured grid solver, USM3D, to obtain solutions for all seven flight conditions of interest. A newly available solver version that incorporates a number of turbulence models, including the two-equation linear and non-linear k-epsilon, was used in this study. As a first test, a choice was made to utilize only a single grid resolution with the solver for the simulation of the different flight conditions. Comparisons are presented with three turbulence models in USM3D, flight data for surface pressure, boundary-layer profiles, and skin-friction results, as well as limited predictions from other solvers. A result of these comparisons is that the USM3D solver can be used in an engineering environment to predict flow physics on a complex configuration at flight Reynolds numbers with a two-equation linear k-epsilon turbulence model.

Lamar, John E.↗
NASA NTRS2018

Generating a Grid for Unstructured RANS Simulations of Jet Flows

A study has been performed to determine best practices for generating unstructured grids for Reynolds-Averaged Navier-Stokes (RANS) simulations of jet flows. The Axisymmetric Near-Sonic Jet Case from the Turbulence Modeling Resource was used for this study: a Mach 0.985 flow through the 2-in. diameter Acoustic Reference Nozzle (ARN2). Simulations were run with FUN3D and used the Menter Shear Stress Transport (SST-V), Spalart-Allmaras (S-A), and k-kL turbulence models. The axial velocity and turbulent kinetic energy fields in the jet plume of the unstructured grid solutions were compared to those of the baseline structured grid solution provided by the Turbulence Modeling Resource. Only solutions using grids with structured-like elements in the jet plume showed good agreement with the baseline structured grid solution. Using the SST-V turbulence model, the fully unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. With the S-A turbulence model, the unstructured grid solutions predicted the jet potential core to decay upstream of the baseline solution. The solutions using the k-kL turbulence model seemed less sensitive to grid topology. Nozzle massflow and thrust performance were also compared for all simulations. Based on the results of this study, it is currently recommended that structured-like grid elements are used in the plumes of jet flows; unstructured grid elements can be used elsewhere.

RANS Simulations; Unstructured Grids; Jet Flows↗
NASA NTRS1992

Interactive solution-adaptive grid generation

TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.

Choo, Yung K.↗
NASA NTRS1993

Three-dimensional Navier-Stokes calculations using solution-adapted grids

A three-dimensional solution-adaptive grid generation technique is presented. The adaptation technique redistributes grid points to improve the accuracy of a flow solution without increasing the number of grid points. It is applicable to structured grids with a multiblock topology. The method uses a numerical mapping and potential theory to modify the initial grid distribution based on the properties of the flow solution on the initial grid. The technique is demonstrated with two examples - a transonic finite wing and a supersonic blunt fin. The advantages are shown by comparing flow solutions on the adapted grids with those on the initial grids.

Henderson, T. L.↗
NASA NTRS1981

Transonic airfoil calculations using solution-adaptive grids

A new algorithm for generating solution-adaptive grids (SAG) about airfoil configurations embedded in transonic flow is presented. The present SAG approach uses only the airfoil surface solution to recluster grid points on the airfoil surface, i.e., the reclustering problem is one dimension smaller than the flow-field calculation problem. Special controls automatically built into the elliptic grid generation procedure are then used to obtain grids with suitable interior behavior. This concept of redistributing grid points greatly simplifies the idea of solution-adaptive grids. Numerical results indicate significant improvements in accuracy for SAG grids relative to standard grids using the same number of points.

Holst, T. L.↗
NASA NTRS1988

Grid embedding technique using Cartesian grids for Euler solutions

Grid-embedding techniques are presently applied to the solutions of the Euler equations on Cartesian grids for the NACA 0012 airfoil and the multielement SKF1.1 airfoil at transonic speeds. Based on comparisons with solutions on fine grids, it is shown that the present scheme, when used in conjunction with the Runge-Kutta time-stepping scheme as well as Cartesian grids, yields reduced memory requirements and a substantial reduction in computational time, without loss of accuracy.

Micheltree, R. A.↗
NASA NTRS1992

Interactive solution-adaptive grid generation procedure

TURBO-AD is an interactive solution adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution adaptive grid generation technique into a single interactive package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on the unit square in the parametric domain, and the new adapted grid is then mapped back to the physical domain. The grid adaption is achieved by adapting the control points to a numerical solution in the parametric domain using control sources obtained from the flow properties. Then a new modified grid is generated from the adapted control net. This process is efficient because the number of control points is much less than the number of grid points and the generation of the grid is an efficient algebraic process. TURBO-AD provides the user with both local and global controls.

Henderson, Todd L.↗
NASA NTRS1992

An Implementation Of The Solution-Adaptive-Grid Method

NASA technical memorandum discusses solution-adaptive-grid method and Self Adaptive Grid Evolution (SAGE) computer code, which implements method. Provides for redistribution of points in grids used to compute flows, especially supersonic and hypersonic flows containing shocks, and other strong gradient regions, discontinuities, and sheer layers. Performed on basis of flow solution obtained on initial grid, then flow recomputed on adapted grid.

Davies, Carol B.↗
NASA NTRS1990

A solution adaptive grid procedure for an upwind parabolized flow solver

A solution adaptive grid procedure based on an error equi-distribution scheme is developed and applied to a Parabolized Navier-Stokes solver. An improved method for selecting weighting functions is introduced which involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point. The scheme re-distributes grid points line-by-line, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions. Torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability. A grid-fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum. Results for several problems are presented to demonstrate the improvements obtainable with the solution adaptive grid procedure.

Harvey, Albert D.↗
NASA NTRS1992

Interactive solution-adaptive grid generation procedure

TURBO-AD is a two dimensional interactive solution adaptive grid generation program. The code uniquely combines a grid adaptation technique that uses parametric mapping with control sources and an algebraic grid generation that uses control points into a single software package. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using the control sources obtained from flow properties. Then a new grid is generated from the adapted control net using the control point formulation. The new adapted grid in the parametric domain is then mapped back to the physical domain. This solution adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the grid generation from the adapted control net is an efficient algebraic process.

Choo, Yung K.↗
NASA NTRS1991

An adaptive grid method for computing time accurate solutions on structured grids

The solution method consists of three parts: a grid movement scheme; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the Euler solver. The grid movement scheme is an algebraic method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling is performed with a grid prediction correction procedure that is simple to implement and provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one dimensional shock tube and a two dimensional shock vortex iteraction.

Bockelie, Michael J.↗
NASA NTRS1991

Application of a solution adaptive grid scheme, SAGE, to complex three-dimensional flows

A new three-dimensional (3D) adaptive grid code based on the algebraic, solution-adaptive scheme of Nakahashi and Deiwert is developed and applied to a variety of problems. The new computer code, SAGE, is an extension of the same-named two-dimensional (2D) solution-adaptive program that has already proven to be a powerful tool in computational fluid dynamics applications. The new code has been applied to a range of complex three-dimensional, supersonic and hypersonic flows. Examples discussed are a tandem-slot fuel injector, the hypersonic forebody of the Aeroassist Flight Experiment (AFE), the 3D base flow behind the AFE, the supersonic flow around a 3D swept ramp and a generic, hypersonic, 3D nozzle-plume flow. The associated adapted grids and the solution enhancements resulting from the grid adaption are presented for these cases. Three-dimensional adaption is more complex than its 2D counterpart, and the complexities unique to the 3D problems are discussed.

Davies, Carol B.↗
NASA NTRS1991

A solution-adaptive grid procedure for the three-dimensional parabolized Navier-Stokes equations

A solution-adaptive grid procedure for the three-dimensional parabolized Navier-Stokes equations is developed on the basis of the two-dimensional line-by-line solution-adaptive technique of Harvey et al. (1990). It is shown that the new adaptive grid algorithm provides improved shock resolving characteristics over the conventional flow algorithm. The adaptation process has the ability of aligning grid lines with the existing flow-field structure, yielding increasing resolution of high gradient regions.

Harvey, Albert D., III↗
NASA NTRS1986

Three-dimensional grids as solutions of elliptic systems

An elliptic grid generation scheme is described which produces a curvilinear, boundary-fitted grid for highly swept wings with sharp leading edges. The three-dimensional integration domain is segmented in successive crossflow sections wherein the physical coordinates are transformed to computational coordinates by solving an elliptic set of two quasi-linear differential equations. Grid points are clustered in the vicinity of the wing surface, especially in the neighborhood of the leading edges. The formulation of the source terms in the equations governing the transformation contains adjustable parameters which are determined from limiting forms of the elliptic equations along the boundaries. The source terms are assigned to each grid point by interpolation of these parameters into the interior domain. The formulation does not depend on the boundary shape or on the distribution of the grid points along the boundaries. For the first time, the discretized governing equations have been solved using a fast AF1 iteration scheme.

Hartwich, P.-M.↗
NASA NTRS1982

The use of solution adaptive grids in solving partial differential equations

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

Anderson, D. A.↗