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Author: Publisher: ISBN: Category : Languages : en Pages : 22
Book Description
The two essential ingredients of any boundary value problem are the field equations which describe the physics of the problem and a set of relations which specify the geometry of the problem domain. Mesh generations or grid generators are preprocessors which decompose the problem domain into a large number of interconnected finite elements or curvilinear finite difference stencils. A number of such techniques have been developed over the pat decade to alleviate the frustration and reduce the time involved in the tedious manual subdividing of a complex-shaped region or 3-D structure into finite elements. Our purpose here is to describe how the techniques of bivariate and trivariate blending function interpolation, which were originally developed for and applied to geometric problems of computer-aided design of sculptured surfaces and 3-D solids, can be adapted and applied to the geometric problems of grid generation. In contrast to other techniques which require the numerical solution of complex partial differential equations (and, hence, a great deal of computing), the transfinite methods proposed herein are computationally inexpensive.
Author: Publisher: ISBN: Category : Languages : en Pages : 22
Book Description
The two essential ingredients of any boundary value problem are the field equations which describe the physics of the problem and a set of relations which specify the geometry of the problem domain. Mesh generations or grid generators are preprocessors which decompose the problem domain into a large number of interconnected finite elements or curvilinear finite difference stencils. A number of such techniques have been developed over the pat decade to alleviate the frustration and reduce the time involved in the tedious manual subdividing of a complex-shaped region or 3-D structure into finite elements. Our purpose here is to describe how the techniques of bivariate and trivariate blending function interpolation, which were originally developed for and applied to geometric problems of computer-aided design of sculptured surfaces and 3-D solids, can be adapted and applied to the geometric problems of grid generation. In contrast to other techniques which require the numerical solution of complex partial differential equations (and, hence, a great deal of computing), the transfinite methods proposed herein are computationally inexpensive.
Author: Vladimir D. Liseikin Publisher: Springer Science & Business Media ISBN: 3662039494 Category : Science Languages : en Pages : 363
Book Description
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.
Author: Vladimir D. Liseikin Publisher: Springer ISBN: 3319578464 Category : Science Languages : en Pages : 541
Book Description
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.
Author: Joe F. Thompson Publisher: CRC Press ISBN: 9781420050349 Category : Technology & Engineering Languages : en Pages : 1136
Book Description
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.
Author: Vladimir D. Liseikin Publisher: Springer Science & Business Media ISBN: 3662054159 Category : Science Languages : en Pages : 274
Book Description
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.
Author: Patrick Knupp Publisher: CRC Press ISBN: 0429605307 Category : Mathematics Languages : en Pages : 312
Book Description
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 Description
This book introduces transfinite interpolation as a generalization of interpolation of data prescribed at a finite number of points to data prescribed on a geometrically structured set, such as a piece of curve, surface, or submanifold. The time-independent theory is readily extended to a moving/deforming data set whose dynamics is specified in a Eulerian or Lagrangian framework. The resulting innovative tools cover a very broad spectrum of applications in fluid mechanics, geometric optimization, and imaging. The authors chose to focus on the dynamical mesh updating in fluid mechanics and the construction of velocity fields from the boundary expression of the shape derivative. Transfinite Interpolations and Eulerian/Lagrangian Dynamics is a self-contained graduate-level text that integrates theory, applications, numerical approximations, and computational techniques. It applies transfinite interpolation methods to finite element mesh adaptation and ALE fluid-structure interaction. Specialists in applied mathematics, physics, mechanics, computational sciences, imaging sciences, and engineering will find this book of interest.
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Author: Vladimir D. Liseikin
Author: Vladimir D. Liseikin
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Author: Jose E. Castillo
Author: Joe F. Thompson
Author: Ross Everett Shaw
Author: Vladimir D. Liseikin
Author: Patrick Knupp
Author: André Garon