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At least 757 records · Page 42

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NASA NTRS1989

Viscous-inviscid interaction and local grid refinement via truncation error injection

A methodology is presented which makes it possible to decouple a complex problem having multiple disparate length scales into problems of single length scale so that they can be solved more efficiently on a computer. The method is applied to a viscous transonic flow over an airfoil. It is found that accurate prediction of the flow over an airfoil can be obtained by solving the Euler equations on a relatively coarse global grid with viscous effects computed separately on a boundary-layer type grid and injected into the global grid solution as a combination of vorticity and trucation error.

Goble, Brian D.↗

NASA NTRS1989

A simplified self-adaptive grid method, SAGE

The formulation of the Self-Adaptive Grid Evolution (SAGE) code, based on the work of Nakahashi and Deiwert, is described in the first section of this document. The second section is presented in the form of a user guide which explains the input and execution of the code, and provides many examples. Application of the SAGE code, by Ames Research Center and by others, in the solution of various flow problems has been an indication of the code's general utility and success. Although the basic formulation follows the method of Nakahashi and Deiwert, many modifications have been made to facilitate the use of the self-adaptive grid method for single, zonal, and multiple grids. Modifications to the methodology and the simplified input options make this current version a flexible and user-friendly code.

Davies, C.↗

NASA NTRS1989

Precise solution for a finite set of spherical coefficients from equiangular gridded data

An important goal of geodesy is to determine the anomalous potential and its derivatives outside of the earth. Representing the surface anomalies by a series of spherical harmonics is useful since it is then possible to do a term by term solution of Laplace's equation and upward continuation. The problem of finding such a spherical harmonic series for anomaly values given on an equiangular surface grid is addressed. (This is a first step toward the more complicated problem of finding a function such that locally averaged values fit a grid of mean anomalies.) Three approaches to this fitting problem are discussed and compared: the discrete Fourier technique, the discrete integral technique, and a new approach. The peculiar nature of the equiangular grid, with its increasing density of (noisy) data toward the poles, causes each method to exhibit a different type of difficulty. The new method is shown to be practical as well as precise since the numerical conditioning problems which appear can be successfully handled by such well-known techniques as a (simple) Kalman filter.

Zucker, Paul A.↗

NASA NTRS1990

Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations

A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.

Johnson, Forrester T.↗

NASA NTRS1990

Stable boundary conditions for Cartesian grid calculations

The inviscid Euler equations in complicated geometries are solved using a Cartesian grid. This requires solid wall boundary conditions in the irregular grid cells near the boundary. Since these cells may be orders of magnitude smaller than the regular grid cells, stability is a primary concern. An approach to this problem is presented and its use is illustrated.

Berger, M. J.↗

NASA NTRS1990

On unstructured grids and solvers

The fundamentals and the state-of-the-art technology for unstructured grids and solvers are highlighted. Algorithms and techniques pertinent to mesh generation are discussed. It is shown that grid generation and grid manipulation schemes rely on fast multidimensional searching. Flow solution techniques for the Euler equations, which can be derived from the integral form of the equations are discussed. Sample calculations are also provided.

Barth, T. J.↗

NASA NTRS1989

Application of a self-adaptive grid method to complex flows

A directional-split modular user-friendly grid-point distribution code is applied to several test problems. Grid-point spacing is determined by user-specified constants denoting maximum and minimum grid spacings and relating the relative influence of smoothness and orthogonality. Estimates of truncation error, in terms of flowfield gradients and/or geometric features, are used to determine the point distribution.

Deiwert, G. S.↗

NASA NTRS1990

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Janus, J. Mark↗

NASA NTRS1990

An embedded grid formulation applied to a delta wing

Applications using a three-dimensional embedded grid scheme are made to high angle of attack viscous flow over two bodies: a slender cone using the conical approximation and a 75 deg swept delta wing. The embedded grids are used principally to improve the numerical resolution of the separated vortical flow above the body. Detailed comparisons are made with experimental measurements of the velocity field over the delta wing. The prediction of the maximum steamwise velocity is improved using two levels of embedded grid refinement but is still less than the experimental measurements available from a laser velocimeter.

Krist, Sherrie L.↗

NASA NTRS1988

Fast interpolation schemes for moving grids

Search algorithms are developed for efficiently locating interpolation points to facilitate transfer of data in moving grid and related problems. Applications in the construction of adaptive grids and in the solution of problems on composite grids are included.

Mastin, C. Wayne↗

NASA NTRS1988

Three-dimensional grid generation about a submarine

A systematic multiple-block grid method has been developed to compute grids about submarines. Several topologies are proposed, and an oscillatory transfinite interpolation is used in the grid construction.

Abolhassani, Jamshid Samareh↗

NASA NTRS1988

Interactive generation of unstructured grids for three dimensional problems

The present interactive grid-generation capability for unstructured grids substantially bases itself on the performance available in the most advanced workstations, in order to obviate much of the input, error-checking, and output process burden associated with the generation of grids in three dimensions. The illustrative examples presented encompass the B-747 wing-fuselage configuration, a generic wing-fuselage-tail pathfinder configuration in a wind tunnel, and a generic train configuration in which surface data are not required to have very high accuracy, but many configurations must be analyzed rapidly.

Lohner, Rainald↗

NASA NTRS1988

Multiple-block grid adaption for an airplane geometry

Grid-adaption methods are developed with the capability of moving grid points in accordance with several variables for a three-dimensional multiple-block grid system. These methods are algebraic, and they are implemented for the computation of high-speed flow over an airplane configuration.

Abolhassani, Jamshid Samareh↗

NASA NTRS1990

An optical technique to measure ion engine grid distortion due to differential thermal expansion

This paper describes an optical technique developed for measuring small differential grid displacements due to thermal expansion of an ion thruster accelerator system. The technique is based on confocal scanning optical microscope type II. For the measurements of small displacements where there are distances on the order of a meter or more between the lens plane and the sample, some of the optical components are moved while the sample is kept fixed. The feasibility of applying this technique to measure the thermally induced ion thruster grid displacements was demonstrated in a bench-top simulation. It is noted that this technique can also provide information on grid movement resulting from thermal transients such as the start-up.

Trava-Airoldi, V. J.↗

NASA NTRS1990

Interactive grid adaption

An interactive grid adaption method is developed, discussed and applied to the unsteady flow about an oscillating airfoil. The user is allowed to have direct interaction with the adaption of the grid as well as the solution procedure. Grid points are allowed to adapt simultaneously to several variables. In addition to the theory and results, the hardware and software requirements are discussed.

Abolhassani, Jamshid S.↗

NASA NTRS1989

SAGE: A 2-D self-adaptive grid evolution code and its application in computational fluid dynamics

SAGE is a user-friendly, highly efficient, two-dimensional self-adaptive grid code based on Nakahashi and Deiwert's variational principles method. Grid points are redistributed into regions of high flowfield gradients while maintaining smoothness and orthogonality of the grid. Efficiency is obtained by splitting the adaption into 2 directions and applying one-sided torsion control, thus producing a 1-D elliptic system that can be solved as a set of tridiagonal equations.

Davies, Carol B.↗

NASA NTRS1990

Development of unstructured grid methods for steady and unsteady aerodynamic analysis

The current status of the development of unstructured grid methods in the Unsteady Aerodynamics Branch at NASA-Langley is described. These methods are being developed for steady and unsteady aerodynamic applications. The flow solvers that were developed for the solution of the unsteady Euler and Navier-Stokes equations are highlighted and selected results are given which demonstrate various features of the capability. The results demonstrate 2-D and 3-D applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy.

Batina, John T.↗

NASA NTRS1991

Development of a grid-independent approximate Riemannsolver

A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.

Rumsey, Christopher Lockwood↗