Application of a variational method for generating adaptive grids
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Kreis, R. I.↗
Engineering topics
Thames, F. C.
Publications and source records attributed to Thames, F. C..
Application of a variational method for generating adaptive grids
The application of variational methods for generating adaptive grids is not as straightforward as one is led to believe. Proper scaling, suitable weight functions and appropriate clustering on boundaries must be employed to obtain a satisfactory grid. This work, which is based on the framework developed by Brackbill and Saltzman, provides simple methods for determining scaling and investigates possible options for selecting the weight function and clustering points on the boundaries. The concepts developed here are applied to two two-dimensional problems: a model problem based on Burger's equation which contains two length scales and, transonic flow past airfoils using the Euler equations.
Kreis, R. I.↗
Multigrid applications to three-dimensional elliptic coordinate generation
The multigrid algorithm was applied to solve the coupled set of elliptic quasilinear partial differential equations associated with three-dimensional coordinate generation. The results indicate that the multigrid scheme is more than twice as fast as conventional relaxation schemes on moderate-size grids. Convergence factors of order 0.90 per work unit were achieved on 36,000-point grids. The paper covers the form of transformation, develops the set of generation equations, and gives details on the multigrid approach used. Included are a development of the full-approximation storage scheme, details of the smoothing-rate analysis, and a section devoted to rational programming techniques applicable to the multigrid algorithm.
Thames, F. C.↗
Generation of three-dimensional boundary-fitted curvilinear coordinate systems for wing/wing-tip geometries using the elliptic solver method
A three-dimensional elliptic solver technique is utilized to generate surface-fitted coordinates about wing/wing-tip configurations. The method is applicable to wings of arbitrary section profile and camber, leading-edge sweep, taper ratio, and spanwise thickness variation. The basic theory of three-dimensional elliptic mappings is developed along with a method to compute interior coordinate control functions. Examples of grids generated about several wing/wing-tip geometries are given. A 49 x 33 x 17 grid requires about 3 minutes of CPU time on a CYBER 203 computer.
Thames, F. C.↗
Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies
A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.
Thompson, J. F.↗
Flow through the tile gaps in the Space Shuttle Thermal Protection System
The problem of predicting aerodynamic loads on the insulating tiles of the Space Shuttle Thermal Protection System (TPS) is discussed and seen to require a method for predicting pressure and mass flux in the gaps between tiles. A mathematical model of the tile-gap flow is developed based upon a slow viscous (Stokes) flow analysis and is verified against available experimental data. This model derives the tile-gap pressure field from a solution of the two-dimensional Laplace equation; the mass flux vector is then calculated from the pressure gradient. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is also given. The flow model shows tile-gap mass flux to be very sensitive to the gap width indicating a need for coupling the TPS flow and tile displacement calculations. Finally recommendations are made concerning additional analytical and experimental work to improve TPS flow predictions.
Dwoyer, D. L.↗
A title-gap flow model for use in aerodynamic loads assessment of space shuttle thermal protection system: Parallel gap faces
The problem of predicting aerodynamic loads on the insulating tiles of the space shuttle thermal protection system (TPS) is discussed and seen to require a method for predicting pressure and mass flux in the gaps between tiles. A mathematical model of the tile-gap flow is developed, based upon a slow viscous (Stokes) flow analysis, and is verified against experimental data. The tile-gap pressure field is derived from a solution of the two-dimensional Laplace equation; the mass-flux vector is then calculated from the pressure gradient. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The means for incorporating this model into a lumped-parameter network analogy for porous-media flow is given. The flow model shows tile-gap mass flux to be very sensitive to the gap width indicating a need for coupling the TPS flow and tile displacement calculation. Analytical and experimental work to improve TPS flow predictions and a possible shuttle TPS hardware modification are recommended.
Dwoyer, D. L.↗
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.↗
Temporal and spatial inconsistencies of time-split finite-difference schemes
The properties of an implicit time-split algorithm, which utilizes locally one dimensional spatial steps, are examined using the two-dimensional heat conduction equation as the test problem. Both temporal and spatial inconsistencies inherent in the scheme are identified. A consistent, implicit splitting approach is developed. The relationship between this method and other time-split implicit schemes is explained, and stability problems encountered with the method in three dimensions are discussed.
Dwoyer, D. L.↗
Accuracy and stability of time-split finite-difference schemes
In a recently published work by Abarbanel and Gottlieb (1980), a new class of explicit time-split algorithms designed for application to the compressible Navier-Stokes equations was developed. These algorithms, which utilize locally-one-dimensional (LOD) spatial steps, were shown to possess stability characteristics superior to those of other time-split schemes. In the present work, the properties of an implicit LOD method, analogous to the Abarbanel-Gottlieb algorithm, are examined using the two-dimensional heat conduction equation as the test problem. Both temporal and spatial inconsistencies inherent in the scheme are identified, and a new consistent, implicit splitting approach is developed and applied to the linear Burgers' equation. The relationship between this new method and other time-split implicit schemes is explained and stability problems encountered with the method in three dimensions are discussed.
Dwoyer, D. L.↗
Properties of aspect-ratio-4.0 rectangular jets in a subsonic crossflow
A series of wind-tunnel and laboratory tests were conducted at the NASA Langley V/STOL tunnel facility to determine both the detailed structure and the induced effects of aspect-ratio-4.0 rectangular jets both in a subsonic crosswind and in quiescent conditions. Wind-tunnel tests were conducted on both blunt (nozzle major axis normal to free stream) and streamwise (nozzle major axis parallel to free stream) nozzle orientations for jet injection angles ranging from 15 to 90 degrees at jet-to-crossflow velocity ratios of 4, 8, and 10. Results indicate that the blunt nozzle induced effects are more significant than those produced by comparable streamwise-oriented jets and that both the flow-field structure and induced effects of streamwise-oriented rectangular jets are quite similar to those created by round jets. Additionally, it is shown that significant differences exist in the vortex flow fields generated by the same rectangular nozzle mounted in two different test hardware configurations.
Thames, F. C.↗
Body-fitted coordinates systems transformations
Two computer programs generate two-dimensional body-fitted coordinate systems and coordinate transformation. Programs are useful in fields requiring accurate numerical representation of boundary conditions and accurate numerical solutions of partial differential equations.
Mastin, C. W.↗
Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies
A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.
Thompson, J. F.↗
Numerical solutions for viscous and potential flow about arbitrary two-dimensional bodies using body-fitted coordinate systems
A procedure for numerical solution of the time-dependent, incompressible Navier-Stokes equations for the flow about arbitrarily shaped two-dimensional bodies is given. This solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having a coordinate line coincident with the body contour regardless of its shape. The implicit solution utilizes the vorticity-stream function formulation with a false-position iterative adjustment of the surface vorticity in satisfaction of the no-slip boundary condition. Excellent agreement with the Blasius boundary layer solution is obtained for a semi-infinite flat plate. Results are presented for Reynolds numbers up to 2000 for several airfoils and a cambered rock.
Thames, F. C.↗
TOMCAT - A code for numerical generation of boundary-fitted curvilinear coordinate systems on fields containing any number of arbitrary two-dimensional bodies
A method for automatic generation of boundary-fitted curvilinear coordinate systems, where the transformed coordinates are solutions of an elliptic differential system in the physical plane, and where the coordinate lines are coincident with all boundaries of a general multiply-connected, two-dimensional region containing any number of arbitrarily shaped bodies, and is described along with a suitable computer code for implementing the method. Any partial differential system can be solved on the boundary-fitted coordinate system by appropriate transformations. The transformed equations are approximated by finite differences and solved numerically in the transformed plane. All computations, whether for generating coordinate system or then solving the transformed equations, can be done on a rectangular field with square mesh with no interpolation required on the boundaries. The physical boundaries may even be time-dependent.
Thompson, J. F.↗
Solutions of the Navier-Stokes equations in various flow regimes on fields containing any number of arbitrary bodies using boundary-fitted coordinate systems
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Thompson, J. T.↗
Use of numerically generated body-fitted coordinate systems for solution of the Navier-Stokes equations
A procedure for numerical solution of the time-dependent, two-dimensional incompressible Navier-Stokes equations that can treat the unsteady laminar flow about bodies of arbitrary shape, such as two-dimensional airfoils, multiple airfoils, and submerged hydrofoils, as naturally as it can deal with the flow about simple bodies. The solution is based on a method of automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multiconnected region containing any number of arbitrarily shaped bodies. The curvilinear coordinates are generated as the solution of two elliptical partial differential equations with Dirichlet boundary conditions, one coordinate being specified to be constant on each of the boundaries, and a distribution of the other being specified along the boundaries. The solution compares excellently with the Blasius boundary layer solution for the flow past a semiinfinite flat plate.
Thompson, J. F.↗
Numerical solution of the Navier-Stokes equations for arbitrary two-dimensional airfoils
A method for numerical solution of the Navier-Stokes equations for the flow about arbitrary airfoils or other bodies is presented. This method utilizes a numerically generated curvilinear coordinate system having a coordinate line coincident with the body contour. Streamlines, velocity profiles, and pressure and force coefficients for several airfoils and an arbitrary rock are given. Potential flow solutions are also presented. The procedure capable of treating multiple-element airfoils, and potential flow results are presented.
Thames, F. C.↗