General Framework For Achieving Textbook Multigrid Efficiency
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General Framework For Achieving Textbook Multigrid Efficiency
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Author :
language : en
Publisher:
Release Date : 2000
General Framework For Achieving Textbook Multigrid Efficiency written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
A general multigrid framework is discussed for obtaining textbook efficiency to solutions of the compressible Euler and Navier-Stokes equations in conservation law form. The general methodology relies on a distributed relaxation procedure to reduce errors in regular (smoothly varying) flow regions; separate and distinct treatments for each of the factors (elliptic and/or hyperbolic) are used to attain optimal reductions of errors. Near boundaries and discontinuities (shocks) additional local relaxations of the conservative equations are necessary. Example calculations are made for the quasi-one-dimensional Euler equations; the calculations illustrate the general procedure.
Multigrid Methods
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Author : Ulrich Trottenberg
language : en
Publisher: Academic Press
Release Date : 2001
Multigrid Methods written by Ulrich Trottenberg and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Frontiers Of Computational Fluid Dynamics 2002
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Author : Robert William MacCormack
language : en
Publisher: World Scientific
Release Date : 2002
Frontiers Of Computational Fluid Dynamics 2002 written by Robert William MacCormack and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Technology & Engineering categories.
This series of volumes on the OC Frontiers of Computational Fluid DynamicsOCO was introduced to honor contributors who have made a major impact on the field. The first volume was published in 1994 and was dedicated to Prof Antony Jameson; the second was published in 1998 and was dedicated to Prof Earl Murman. The volume is dedicated to Prof Robert MacCormack. The twenty-six chapters in the current volume have been written by leading researchers from academia, government laboratories, and industry. They present up-to-date descriptions of recent developments in techniques for numerical analysis of fluid flow problems, and applications of these techniques to important problems in industry, as well as the classic paper that introduced the OC MacCormack schemeOCO to the world. Contents: The Effect of Viscosity in Hypervelocity Impact Cratering (R W MacCormack); The MacCormack Method OCo Historical Perspective (C M Hung et al.); Numerical Solutions of Cauchy-Riemann Equations for Two and Three Dimensional Flows (M M Hafez & J Houseman); Extension of Efficient Low Dissipation High Order Schemes for 3-D Curvilinear Moving Grids (M Vinokur & H C Yee); Scalable Parallel Implicit Multigrid Solution of Unsteady Incompressible Flows (R Pankajakshan et al.); Lattice Boltzmann Simulation of Incompressible Flows (N Satofuka & M Ishikura); Numerical Simulation of MHD Effects on Hypersonic Flow of a Weakly Ionized Gas in an Inlet (R K Agarwal & P Deb); Development of 3D DRAGON Grid Method for Complex Geometry (M-S Liou & Y Zheng); Advances in Algorithms for Computing Aerodynamic Flows (D W Zingg et al.); Selected CFD Capabilities at DLR (W Kordulla); CFD Applications to Space Transportation Systems (K Fujii); Information Science OCo A New Frontier of CFD (K Oshima & Y Oshima); Integration of CFD into Aerodynamics Education (E M Murman & A Rizzi); and other papers. Readership: Researchers and graduate students in numerical and computational mathematics."
Multiscale And Multiresolution Methods
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Author : Timothy J. Barth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiscale And Multiresolution Methods written by Timothy J. Barth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.
Recent Advances In Achieving Textbook Multigrid Efficiency For Computational Fluid Dynamics Simulations
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Author : Achi Brandt
language : en
Publisher:
Release Date : 2002
Recent Advances In Achieving Textbook Multigrid Efficiency For Computational Fluid Dynamics Simulations written by Achi Brandt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Recent advances in achieving textbook multigrid efficiency for fluid simulations are presented. Textbook multigrid efficiency is defined as attaining the solution to the governing system of equations in a computational work which is a small multiple of the operation counts associated with discretizing the system. Strategies are reviewed to attain this efficiency by exploiting the factorizability properties inherent to a range of fluid simulations, including the compressible Navier-Stokes equations. factorizability is used to separate the elliptic and hyperbolic factors contributing to the target system; each of the factors can then be treated individually and optimally. Boundary regions and discontinuities are addressed with separate (local) treatments. New formulations and recent calculations demonstrating the attainment of textbook efficiency for aerodynamic simulations are shown.
Siam Journal On Scientific Computing
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Author :
language : en
Publisher:
Release Date : 2004
Siam Journal On Scientific Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Electronic journals categories.
Analysis Of Boundary Conditions For Factorizable Discretizations Of The Euler Equations
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Author : Boris Diskin
language : en
Publisher:
Release Date : 2002
Analysis Of Boundary Conditions For Factorizable Discretizations Of The Euler Equations written by Boris Diskin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
In this article, several sets of boundary conditions or factorizable schemes corresponding to the steady-state compressible Euler equations are evaluated. The analyzed model is a one-dimensional constant-coefficient problem. Numerical tests have been performed for a fully subsonic quasi-one-dimensional flow in a convergent/divergent channel. This paper focuses on the effect of boundary-condition equations on stability and accuracy of the discrete solutions. Explicit correspondence between solutions and boundary conditions is established through a boundary-condition-sensitivity (BCS) matrix. The following new findings are reported: (1) Examples of stable discrete problems contradicting a wide-spread belief that employment of a one-order-lower approximation schemes in an O(h)-small region does not affect the overall accuracy order of the solution have been found and explained. Such counterexamples can only be constructed for systems of differential equations. For scalar equations, the conventional wisdom is correct. (2) A negative effect of overspecified (although, exact) boundary conditions on accuracy and stability of the solution has been observed and explained. (3) Sets of practical boundary conditions for factorizable schemes providing stable second-order accurate solutions have been formulated. These schemes belong to a family of second-order schemes requiring second-order accuracy for some numerical-closure boundary conditions.
Nasa Langley Scientific And Technical Information Output 2000
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Author :
language : en
Publisher:
Release Date : 2001
Nasa Langley Scientific And Technical Information Output 2000 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Activities Of Institute For Computer Applications In Science And Engineering Icase
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Author :
language : en
Publisher:
Release Date : 2001
Activities Of Institute For Computer Applications In Science And Engineering Icase written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
New Factorizable Discretizations For The Euler Equations
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Author : Boris Diskin
language : en
Publisher:
Release Date : 2002
New Factorizable Discretizations For The Euler Equations written by Boris Diskin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
A multigrid method is defined as having textbook multigrid efficiency (TME) if solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. Away to achieve TME for the Euler and Navier-Stokes equations is to apply the distributed relaxation method thereby separating the elliptic and hyperbolic partitions of the equations. Design of a distributed relaxation scheme can be significantly simplified if the target discretization possesses two properties: (1) factorizability, and (2) consistent approximations for the separate factors. The first property implies that the discrete system determinant can be represented as a product of discrete factors, each of them approximating a corresponding factor of the determinant of the differential equations. The second property requires that the discrete factors reflect the physical anisotropies, be stable, and be easily solvable. In this paper, discrete schemes for the nonconservative Euler equations possessing properties (1) and (2) have been derived and analyzed. The accuracy of these scheme has been tested for subsonic flow regimes and is comparable with the accuracy of standard schemes. TME has been demonstrated in solving fully subsonic quasi-one-dimensional flow in a convergent/divergent channel.