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At least 1,243 records · Page 69
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NASA NTRS1986

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. Previous derivations of these matrices have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The present work derives differentiating matrices on grids with arbitrarily spaced points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids through the expedient of including 'near boundary' points. Use of the differentiating matrix as an operator in the solution of problems involving ordinary differential equations is also considered.

Lakin, W. D.↗
NASA NTRS1986

Three-dimensional, conservative, Euler computations using patched grid systems and explicit methods

The method of 'zonal approach' (in which the flow field is partitioned into regions with independent grids) for computation of flow over complex geometries, such as aircraft configuration, requires application of a grid-interfacing procedure. A three-dimensional conservative, boundary scheme for patched grids, applicable in generalized coordinates for arbitrary point distributions on a planar zonal surface is presented. The computation technique is derived within the framework of the Osher (1983) upwind scheme, using Euler equations. The three-dimensional interfacing method is applied to the computation of flow about a wing-canard combination using a two-zone, patched grid.

Hessenius, K. A.↗
NASA NTRS1986

Slow crack growth measurement using an electrical grid

Photolithography was used to produce a resistance grid on the surface of a DCB fracture specimen. The grid line spacings were 10 microns over a distance of 2 cm. Slow crack growth was measured on soda-lime-silica glass. At low values of K(I) (0.3 to 0.4 MPa.sq r + m, increased. Equations are given for the design of grids. The grid technique could be used to measure very slow crack growth at high temperature with appropriate compatible metal-ceramic materials.

Martin, D. J.↗
NASA NTRS1987

Conservative zonal schemes for patched grids in 2 and 3 dimensions

The computation of flow over complex geometries, such as realistic aircraft configurations, poses difficult grid generation problems for computational aerodynamicists. The creation of a traditional, single-module grid of acceptable quality about an entire configuration may be impossible even with the most sophisticated of grid generation techniques. A zonal approach, wherein the flow field is partitioned into several regions within which grids are independently generated, is a practical alternative for treating complicated geometries. This technique not only alleviates the problems of discretizing a complex region, but also facilitates a block processing approach to computation thereby circumventing computer memory limitations. The use of such a zonal scheme, however, requires the development of an interfacing procedure that ensures a stable, accurate, and conservative calculation for the transfer of information across the zonal borders.

Hessenius, Kristin A.↗
NASA NTRS1987

Geometric description and grid generation for space vehicles

The understanding and analysis of three dimensional fluid behavior around reentry vehicles, like the Space Shuttle Orbiter, is of considerable importance for flight applications. Vehicle designers need pressure, heat transfer, and shear distributions to support design activities. Traditionally these have been obtained by experimental data. Significant reduction in design costs can be obtained if the calculated results based on finite difference procedures are used to verify and supplement experimental results. Computing the flow field over Space Shuttle Orbiter, which has complex cross sectional geometries is a major problem. A first step in this direction is development of body definition and grid generation procedure. In this project a digitized body definition and grid generation procedure, developed earlier at JSC, is modified and applied to the Shuttle Orbiter X24C-10D. Two dimensional grid and body definition for various sections of the space vehicle is obtained using the differential equation method. This study demonstrates that this geometry and grid generation procedure can be applied to other aerospace vehicles such as aerospaceplanes.

Krishna, Madakasira G.↗
NASA NTRS1987

High resolution finite volume methods on arbitrary grids via wave propagation

A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.

Leveque, Randall J.↗
NASA NTRS1988

Three-dimensional adaptive grid generation for body-fitted coordinate system

This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.

Chen, S. C.↗
NASA NTRS1988

Three dimensional grid generation for complex configurations: Recent progress

Some of the capabilities of the Computational Fluid Dynamics (CFD) community are surveyed for griding complex three dimensional configurations. The intent is to provide some insight as to the present state of grid generation for aircraft configurations in order to help assess whether this task presents a long term stumbling block to routine use of CFD in aerodynamic applications. A brief review is given of some of the techniques that are available for generating body conforming curvilinear grids. In order to assess capabilities in grid generation, colleagues at selected institutions were solicited to describe their experiences and difficulties in grid generation of complex configurations.

J.F. Thompson↗
NASA NTRS1988

Grid generation on and about a cranked-wing fighter aircraft configuration

Experiences at the NASA Langley Research Center generating grids about a cranked wing fighter aircraft configuration is described. A single block planar grid about the fuselage and canard used with a finite difference Navier-Stokes solver is also described. A dual block nonplanar grid about the complete configuration and used with a finite volume Euler solver is presented. The very important aspect of computing the aircraft surface grid, starting with a standardized model description, is also presented.

Smith, Robert E.↗
NASA NTRS1986

Interface procedures for overlapping grids

The solution of partial differential equations by means of either implicit or conservative explicit finite-difference methods, on the one hand, or multicomponent overlapping grid schemes on the other, is presently subjected to interpolation at grid boundaries in an attempt to eliminate the time lag. The accuracy of the transient solution of a hyperbolic or parabolic partial differential equation is dependent on the procedures used to transfer information between grids in a composite grid system. The present techniques reduce numerical solution errors.

Mastin, C. Wayne↗
NASA NTRS1988

Incompressible and anelastic flow simulations on numerically generated grids

In the numerical simulation of incompressible and anelastic flows, it is necessary to solve an elliptic equation at each time step. When the boundaries of such flows are nonrectangular, it may be advantageous to solve the equations on a new, numerically generated coordinate grid, in which the property of orthogonality has been preserved. Flow equations in general curvilinear coordinates maintaining the conservative form are given for both anelastic models using the momentum equations, and for incompressible models, using the vorticity equation. The general problem of grid-generation in two dimensions is presented, and a quasi-conformal transformation technique is discussed in detail. Some examples of grids generated by this technique are exhibited. Three examples of the flow of a stratified fluid over obstacles are presented, in which the grid-generation permits some new results to be obtained.

Sharman, R. D.↗
NASA NTRS1988

Grid oscillators

Loading a two-dimensional grid with active devices offers a means of combining the power of solid-state oscillators in the microwave and millimeter-wave range. The grid structure allows a large number of negative resistance devices to be combined. This approach is attractive because the active devices do not require an external locking signal, and the combining is done in free space. In addition, the loaded grid is a planar structure amenable to monolithic integration. Measurements on a 25-MESFET grid at 9.7 GHz show power-combining and frequency-locking without an external locking signal, with an ERP of 37 W. Experimental far-field patterns agree with theoretical results obtained using reciprocity.

Popovic, Zorana B.↗
NASA NTRS1988

High resolution finite volume methods on arbitrary grids via wave propagation

A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Rieman problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.

Leveque, Randall J.↗
NASA NTRS1989

Navier-Stokes Calculations With Deforming Grid

Scheme for numerical simulation of transonic, compressible, viscous flow about two-dimensional cascade of oscillating rigid airfoils involves finite-difference solution of Navier-Stokes equations on coordinate grid deforming with motions of airfoils. Contributes to understanding of flows around advanced turboprop airfoil sections. Cascade represented by periodic grid conforming to airfoils and to outer boundaries. Oscillation of airfoil represented by deformation of grid. Applications of deforming-grid technique includes turbomachinery and aeroelastic modeling of nonrigid airfoils.

Huff, Dennis L.↗
NASA NTRS1989

Evaluation of the Dornier Gmbh interactive grid generation system

An interactive grid generation program, INGRID, is investigated and evaluated. A description of the task and work performed, a description and evaluation of INGRID, and a discussion of the possibilities for bringing INGRID into the NASA and Numerical Aerodynamic Simulator (NAS) computing environments is included. The interactive grid generation program was found to be a viable approach for grid generation and determined that it could be converted to work in the NAS environment but that INGRID does not solve the fundamentally hard problems associated with grid generation, specifically, domain decomposition.

Brown, Robert L.↗
NASA NTRS1989

Efficient grid generation

Because the governing equations in fluid dynamics contain partial differentials and are too difficult in most cases to solve analytically, these differentials are generally replaced by finite difference terms. These terms contain terms in the solution at nearby states. This procedure discretizes the field into a finite number of states. These states, when plotted, form a grid, or mesh, of points. It is at these states, or field points, that the solution is found. The optimum choice of states, the x, y, z coordinate values, minimizes error and computational time. But the process of finding these states is made more difficult by complex boundaries, and by the need to control step size differences between the states, that is, the need to control the spacing of field points. One solution technique uses a different set of state variables, which define a different coordinate system, to generate the grid more easily. A new method, developed by Dr. Joseph Steger, combines elliptic and hyperbolic partial differential equations into a mapping function between the physical and computational coordinate systems. This system of equations offers more control than either equation provides alone. The Steger algorithm was modified in order to allow bodies with stronger concavities to be used, offering the possibility of generating a single grid about multiple bodies. Work was also done on identifying areas where grid breakdown occurs.

Seki, Rycichi↗
NASA NTRS1988

Millimeter-wave diode-grid frequency doubler

Monolithic diode grids were fabricated on 2-cm square gallium-arsenide wafers in a proof-of-principle test of a quasi-optical varactor millimeter-wave frequency multiplier array concept. An equivalent circuit model based on a transmission-line analysis of plane wave illumination was applied to predict the array performance. The doubler experiments were performed under far-field illumination conditions. A second-harmonic conversion efficiency of 9.5 percent and output powers of 0.5 W were achieved at 66 GHz when the diode grid was pumped with a pulsed source at 33 GHz. This grid had 760 Schottky-barrier varactor diodes. The average series resistance was 27 ohms, the minimum capacitance was 18 fF at a reverse breakdown voltage of -3 V. The measurements indicate that the diode grid is a feasible device for generating watt-level powers at millimeter frequencies and that substantial improvement is possible by improving the diode breakdown voltage.

Jou, Christina F.↗
NASA NTRS1988

An interactive grid generation technique for fighter aircraft geometries

This paper describes an interactive procedure to construct grids about fighter aircraft using a state-of-the-art workstation. The aircraft are characterized by a fuselage with an integrated canopy over the cockpit, an engine inlet, an area ruled midsection, canards, and highly-swept cranked delta wings or strakes integrated into the wings and tail surfaces. The grid topology, configuration surface grid, exterior grid computation, and computational interactive process are addressed.

Smith, Robert E.↗