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Grid Generation For The Solution Of Partial Differential Equations
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Book Synopsis Fundamentals of Grid Generation by : Patrick Knupp
Download or read book Fundamentals of Grid Generation written by Patrick Knupp and published by CRC Press. This book was released on 2020-12-17 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Grid Generation is an outstanding text/reference designed to introduce students in applied mathematics, mechanical engineering, and aerospace engineering to structured grid generation. It provides excellent reference material for practitioners in industry, and it presents new concepts to researchers. Readers will learn what boundary-conforming grids are, how to generate them, and how to devise their own methods. The text is written in a clear, intuitive style that doesn't get bogged down in unnecessary abstractions. Topics covered include planar, surface, and 3-D grid generation; numerical techniques; solution adaptivity; the finite volume approach to discretization of hosted equations; concepts from elementary differential geometry; and the transformation of differential operators to general coordinate systems. The book also reviews the literature on algebraic, conformal, orthogonal, hyperbolic, parabolic, elliptic, biharmonic, and variational approaches to grid generation. This unique volume closes with the author's original methods of variational grid generation.
Book Synopsis Grid Generation for the Solution of Partial Differential Equations by : Institute for Computer Applications in Science and Engineering
Download or read book Grid Generation for the Solution of Partial Differential Equations written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1987 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Grid Generation by : Joe F. Thompson
Download or read book Handbook of Grid Generation written by Joe F. Thompson and published by CRC Press. This book was released on 1998-12-29 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Grid Generation addresses the use of grids (meshes) in the numerical solutions of partial differential equations by finite elements, finite volume, finite differences, and boundary elements. Four parts divide the chapters: structured grids, unstructured girds, surface definition, and adaption/quality. An introduction to each section provides a roadmap through the material. This handbook covers: Fundamental concepts and approaches Grid generation process Essential mathematical elements from tensor analysis and differential geometry, particularly relevant to curves and surfaces Cells of any shape - Cartesian, structured curvilinear coordinates, unstructured tetrahedra, unstructured hexahedra, or various combinations Separate grids overlaid on one another, communicating data through interpolation Moving boundaries and internal interfaces in the field Resolving gradients and controlling solution error Grid generation codes, both commercial and freeware, as well as representative and illustrative grid configurations Handbook of Grid Generation contains 37 chapters as well as contributions from more than 100 experts from around the world, comprehensively evaluating this expanding field and providing a fundamental orientation for practitioners.
Book Synopsis A Computational Differential Geometry Approach to Grid Generation by : Vladimir D. Liseikin
Download or read book A Computational Differential Geometry Approach to Grid Generation written by Vladimir D. Liseikin and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems. In an updated and expanded Second Edition, this monograph gives a detailed treatment based on the numerical solution of inverted Beltramian and diffusion equations with respect to monitor metrics for generating both structured and unstructured grids in domains and on surfaces.
Book Synopsis Grid Generation Methods by : Vladimir D. Liseikin
Download or read book Grid Generation Methods written by Vladimir D. Liseikin and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.
Book Synopsis Basic Structured Grid Generation by : M Farrashkhalvat
Download or read book Basic Structured Grid Generation written by M Farrashkhalvat and published by Elsevier. This book was released on 2003-02-11 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element, finite volume and finite difference methods use grids to solve the numerous differential equations that arise in the modelling of physical systems in engineering. Structured grid generation forms an integral part of the solution of these procedures. Basic Structured Grid Generation provides the necessary mathematical foundation required for the successful generation of boundary-conforming grids and will be an important resource for postgraduate and practising engineers.The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques. A practical, straightforward approach to this complex subject for engineers and students. A key technique for modelling physical systems.
Book Synopsis Adaptive Grid Generation for Numerical Solution of Partial Differential Equations by : K. G. Brown
Download or read book Adaptive Grid Generation for Numerical Solution of Partial Differential Equations written by K. G. Brown and published by . This book was released on 1983 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach for the generation of flow-adaptive grids for numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numerical evaluation of any partial differential equation. The dynamic coupling of the grid with the flow solution is accomplished through a grid-optimization technique. The optimization is based on the minimization of the finite difference truncation error in the transformed plane. The method is tested on the one-dimensional Burgers' equation which is representative of typical fluid dynamics problems. Burgers' equation is solved with an optimized SOR (Successive Over Relaxation) method using upwind difference for the convective term. Results are presented for various Reynolds numbers and are compared to results from a similar adaptive grid method and to results for a static grid. They show the ability of the method to concentrate grid points high in gradient regions where large truncation errors occur. (Author).
Book Synopsis Adaptive Grid Generation for Numerical Solution of Partial Differential Equations by : Kevin G. Brown (1LT, USAF.)
Download or read book Adaptive Grid Generation for Numerical Solution of Partial Differential Equations written by Kevin G. Brown (1LT, USAF.) and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Grid Generation by : Joe F. Thompson
Download or read book Numerical Grid Generation written by Joe F. Thompson and published by North Holland. This book was released on 1985 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Problem Controlled Grid Generation for the Numerical Solution of Partial Differential Equations by : Paul S. Jensen
Download or read book Problem Controlled Grid Generation for the Numerical Solution of Partial Differential Equations written by Paul S. Jensen and published by . This book was released on 1975 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conventional finite element analysis of elliptic partial differential equations involves the establishment of a discretization grid on which an energy functional is defined and minimized. By including the positions of the grid nodes as unknowns in the energy functional, one can obtain the optimum placement of the nodes as well as the equation solution from the energy minimization. The potential of Chebyshev iterate acceleration in the inverse iteration eigensolution process has long been understood but not realized in practical applications. Its potential is readily realized in the sectioning algorithm by virtue of the fixed interval over which analysis is made.
Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781723040085 Total Pages :126 pages Book Rating :4.0/5 (4 download)
Book Synopsis Efficient Grid Generation by : National Aeronautics and Space Administration (NASA)
Download or read book Efficient Grid Generation written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-18 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Unspecified Center COMPUTATIONAL FLUID DYNAMICS; COMPUTATIONAL GRIDS; GRID GENERATION (MATHEMATICS); HYPERBOLIC DIFFERENTIAL EQUATIONS; ALGORITHMS; PARTIAL DIFFERENTIAL EQUATIONS; TRANSFORMATIONS (MATHEMATICS)...
Book Synopsis Mathematical Aspects of Numerical Grid Generation by : Jos E. Castillo
Download or read book Mathematical Aspects of Numerical Grid Generation written by Jos E. Castillo and published by SIAM. This book was released on 1991-01-01 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical grid generation plays a critical role in any scientific computing problem when the geometry of the underlying region is complex or when the solution has a complex structure. The mathematical aspects of grid generation are discussed to provide a deeper understanding of the algorithms and their imitations. Variational methods are emphasized because they are more robust, but elliptic and transcendental algebraic methods are also considered.
Book Synopsis Numerical Grid Generation in Computational Fluid Dynamics by : J. Ha user
Download or read book Numerical Grid Generation in Computational Fluid Dynamics written by J. Ha user and published by . This book was released on 1986 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Workshop on Numerical Grid Generation Techniques for Partial Differential Equations by :
Download or read book Workshop on Numerical Grid Generation Techniques for Partial Differential Equations written by and published by . This book was released on 1980 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Grid generation about airfoils using multigrid methods in the solution of elliptic partial differential equations by : Romesh Kumar Jain
Download or read book Grid generation about airfoils using multigrid methods in the solution of elliptic partial differential equations written by Romesh Kumar Jain and published by . This book was released on 1986 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Grid Generation about Airfoils Using Multigrid Methods in the Solution of Elliptic Partial Differential Equations by : Kumar Romesh Jain
Download or read book Grid Generation about Airfoils Using Multigrid Methods in the Solution of Elliptic Partial Differential Equations written by Kumar Romesh Jain and published by . This book was released on 1986 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Grid Generation about airfoils using multgrid methods in the solution of elliptic partial differential equations by :
Download or read book Grid Generation about airfoils using multgrid methods in the solution of elliptic partial differential equations written by and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
