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  • 1
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    Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies (1974)
    In:  Other Sources
    Details
    Publication Date: 2011-08-16
    Description: A method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected region containing any number of arbitrarily shaped bodies is presented. 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. Numerical solutions for the lifting and nonlifting potential flow about Joukowski and Karman-Trefftz airfoils using this coordinate system generation show excellent comparison with the analytic solutions. The application to fields with multiple bodies is illustrated by a potential flow solution for multiple airfoils.
    Keywords: AERODYNAMICS
    Type: Journal of Computational Physics; 15; July 197
    Format: text
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  • 2
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    Interface procedures for overlapping grids (1985)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Interpolation at grid boundaries is studied for the purpose of solving partial differential equations using either implicit or conservative explicit finite-difference methods on multi-component overlapping grid systems.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-176460 , NAS 1.26:176460
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  • 3
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    Adaptive EAGLE dynamic solution adaptation and grid quality enhancement (1992)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: In the effort described here, the elliptic grid generation procedure in the EAGLE grid code was separated from the main code into a subroutine, and a new subroutine which evaluates several grid quality measures at each grid point was added. The elliptic grid routine can now be called, either by a computational fluid dynamics (CFD) code to generate a new adaptive grid based on flow variables and quality measures through multiple adaptation, or by the EAGLE main code to generate a grid based on quality measure variables through static adaptation. Arrays of flow variables can be read into the EAGLE grid code for use in static adaptation as well. These major changes in the EAGLE adaptive grid system make it easier to convert any CFD code that operates on a block-structured grid (or single-block grid) into a multiple adaptive code.
    Keywords: AERODYNAMICS
    Type: California State Univ., The Fifth Symposium on Numerical and Physical Aspects of Aerodynamic Flows; 13 p
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  • 4
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    Parameterization in Grid Generation (1985)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The distribution of grid points for calculating the solution of partial differential equations is chosen so as to include consideration of truncation error, stability, and the resolution of the solution near boundary layers and shocks. It is important to specify the distribution of points along a grid line. The problem of distributing points along a curve is considered. It is assumed that the curve is defined parametrically. The objective is to select a set of parameter values so that the corresponding points on the curves are properly distributed. The distribution is based on some intrinsic property of the curve such as arc length or curvature.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA. Langley Research Center Computational Geometry and Computer-Aided Design; p 83-86
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  • 5
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    Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review (1982)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.
    Keywords: NUMERICAL ANALYSIS
    Type: Journal of Computational Physics (ISSN 0021-9991); 47; July 198
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  • 6
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    Experience in grid optimization (1987)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: Two optimization methods for solving a variational problem in grid generation are described and evaluated. The smoothness, cell volumes, and orthogonality of the variational integrals are examined. The Jacobi-Newton iterative method is compared to the Fletcher-Reeves conjugate gradient method. It is observed that a combination of the Jacobi-Newton iteration and the direct solution of the variational problem produces an algorithm which is easy to program and requires less storage and computer time/iteration than the conjugate gradient method.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA PAPER 87-0201
    Format: text
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  • 7
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    Quasiconformal mappings and grid generation (1983)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: A finite difference scheme is developed for constructing quasiconformal mappings for arbitrary simply and doubly connected regions. Computational grids are generated to reduce elliptic equations to canonical form. Examples of conformal mappings on surfaces are also included.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-173920 , NAS 1.26:173920
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  • 8
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    Grid generation using differential systems techniques (1980)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The errors in approximating the derivatives of a function by traditional central differences at grid points of a curvilinear coordinate system were examined. The implications concerning the accuracy of the numerical solution of a partial differential equation are explained by considering several numerical examples. Although this study only considers the two dimensional case, the techniques and implications are equally valid for three dimensional grids. An interesting feature of the error analysis is its simplicity. Most of the results follow by merely working with the truncation terms of some power series expansion. These series expansions also give rise to higher order difference approximations which can significantly reduce error when the grid spacing changes rapidly, as might be the case in problems with shock waves or thin boundary layers.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA. Langley Research Center Numerical Grid Generation Tech.; p 37-72
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  • 9
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    Transformation of three-dimensional regions into rectangular regions by elliptic systems (1976)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-CR-153331 , ICASE-76-13
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  • 10
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    Mesh generation by conformal and quasiconformal mappings (1981)
    In:  Other Sources
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    Publication Date: 2019-06-28
    Description: It is pointed out that many recent advances in the finite-difference solution of elliptic equations have been limited to regions whose boundary contours coincide with coordinate lines of the Cartesian coordinate system. The reason for this is related to the fact that in the case of an arbitrary curvilinear coordinate system the original equation becomes much more complex. However, there is no added complexity if an orthogonal coordinate system is generated from a conformal mapping. In the present investigation, a finite difference method developed for the construction of conformal mappings has been generalized to construct quasi-conformal mappings. It is expected that the use of more sophisticated numerical algorithms could lead to improvements in both speed and accuracy. Quasi-conformal mappings have applications not only in the solution of elliptic equations but also in other areas such as orthogonal mesh generation on surfaces and the solution of certain fluid flow problems.
    Keywords: NUMERICAL ANALYSIS
    Format: text
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