Conservative finitedifference methods on general grids
 Responsibility
 by Mikhail Shashkov and Stanly Steinberg.
 Imprint
 Boca Raton : CRC Press, 1996.
 Physical description
 359 p, : ill. ; 24 cm. + 1 computer disk (3 1/2 in.)
 Series
 Symbolic and numeric computation series
Online
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Call number  Note  Status 

QA431 .S484 1996  Available 
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Description
Creators/Contributors
 Author/Creator
 Shashkov, Mikhail.
 Contributor
 Steinberg, Stanly.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 INTRODUCTION Governing Equations Elliptic Equations Heat Equation Equation of Gas Dynamic in Lagrangian Form The Main Ideas of FiniteDifference Algorithms 1D Case 2D Case Methods of Solution of Systems of Linear Algebraic Equation Methods of Solution of Systems of Nonlinear Equations METHOD OF SUPPORTOPERATORS Main Stages The Elliptic Equations Gas Dynamic Equations System of Consistent Difference Operators in 1D Inner Product in Spaces of Difference Functions and Properties of Difference Operators System of Consistent Difference Operators in 2D THE ELLIPTIC EQUATIONS Introduction Continuum Elliptic Problems with Dirichlet Boundary Conditions Continuum Elliptic Problems with Robin Boundary Conditions OneDimensional Support Operator Algorithms Nodal Discretization of Scalar Functions and CellCentered Discretization of Vector Functions CellValued Discretization of Scalar Functions and Nodal Discretization of Vector Functions Numerical Solution of Test Problems TwoDimensional Support Operator Algorithms Nodal Discretization of Scalar Functions and CellValued Discretization of Vector Functions CellValued Discretization of Scalar Functions and Nodal Discretization of Vector Functions Numerical Solution of Test Problems Conclusion TwoDimensional Support Operator Algorithms Discretization Spaces of Discrete Functions The Prime Operator The Derived Operator Multiplication by a Matrix and the Operator D The Difference Scheme for the Elliptic Operator The Matrix Problem Approximation and Convergence Properties HEAT EQUATION Introduction FiniteDifference Schemes for Heat Equation in 1D FiniteDifference Schemes for Heat Equation in 2D LAGRANGIAN GAS DYNAMICS Kinematics of Fluid Motions Integral Form of Gas Dynamics Equations Integral Equations for One Dimensional Case Differential Equations of Gas Dynamics in Lagrangian Form The Differential Equations in 1D. Lagrange Mass Variables The Statements of Gas Dynamics Problems in Lagrange Variables Different Forms of Energy Equation Acoustic Equations Reference Information Characteristic Form of Gas Dynamics Equations Riemann's Invariants Discontinuous Solutions Conservation Laws and Properties of First Order Invariant Operators FiniteDifference Algorithm in 1D Discretization in 1D Discrete Operators in 1D SemiDiscrete FiniteDifference Scheme in 1D Fully Discrete, Explicit, Computational Algorithm Computational AlgorithmNew Time StepExplicit FiniteDifference Scheme Computational AlgorithmNew Time StepImplicit FiniteDifference Scheme Stability Conditions Homogeneous FiniteDifference Schemes. Artificial Viscosity Artificial Viscosity in 1D Numerical Example Finite Difference Algorithm in 2D Discretization in 2D Discrete Operators in 2D SemiDiscrete FiniteDifference Scheme in 2D Stability Conditions FiniteDifference Algorithm in 2D Computational AlgorithmNew Time StepExplicit FiniteDifference Scheme Computational AlgorithmNew Time StepImplicit FiniteDifference Scheme Artificial Viscosity in 2D Numerical Example APPENDIX: FORTRAN CODE DIRECTORY General Description of Structure of Directories on the Disk Programs for Elliptic Equations Programs for 1D Equations Programs for 2D Equations Programs for Heat Equations Programs for 1D Equations Programs for 2D Equations Programs for Gas Dynamics Equations Programs for 1D Equations Programs for 2D Equations Bibliography.
 (source: Nielsen Book Data)
 Publisher's summary

This new book deals with the construction of finitedifference (FD) algorithms for three main types of equations: elliptic equations, heat equations, and gas dynamic equations in Lagrangian form. These methods can be applied to domains of arbitrary shapes. The construction of FD algorithms for all types of equations is done on the basis of the supportoperators method (SOM). This method constructs the FD analogs of main invariant differential operators of first order such as the divergence, the gradient, and the curl. This book is unique because it is the first book not in Russian to present the supportoperators ideas.Conservative FiniteDifference Methods on General Grids is completely selfcontained, presenting all the background material necessary for understanding. The book provides the tools needed by scientists and engineers to solve a wide range of practical engineering problems. An abundance of tables and graphs support and explain methods. The book details all algorithms needed for implementation. A 3.5" IBM compatible computer diskette with the main algorithms in FORTRAN accompanies text for easy use.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 1996
 ISBN
 0849373751 (alk. paper)
 9780849373756 (alk. paper)