000 09997cam 22003854a 45e0
001 1291087
005 20060322124032.0
008 011016s2002 enka b 001 0 eng
010 $a 2001052642
035 $a(OCoLC)ocm48221422
040 $aDLC$cDLC$dC#P
020 $a0521810876
020 $a0521009243 (pb.)
042 $apcc
050 00 $aQA377$b.L41566 2002
082 00 $a515/.353$221
049 $aIPL1
100 1 $aLeVeque, Randall J.,$d1955-
245 10 $aFinite volume methods for hyperbolic problems
/$cRandall J. LeVeque.
260 $aCambridge ;$aNew York :$bCambridge University
Press,$c2002.
300 $axix, 558 p. :$bill. ;$c25 cm.
440 0 $aCambridge texts in applied mathematics
504 $aIncludes bibliographical references (p. 535-552)
and index.
505 00 $tConservation Laws --$tFinite Volume Methods
--$tMultidimensional Problems --$tLinear Waves and
Discontinuous Media --$tClawpack Software --$tLinear
Equations --$tConservation Laws and Differential Equations
--$tThe Advection Equation --$tDiffusion and the
Advection-Diffusion Equation --$tThe Heat Equation
--$tCapacity Functions --$tNonlinear Equations in Fluid
Dynamics --$tLinear Acoustics --$tSound Waves
--$tHyperbolicity of Linear Systems --$tVariable-Coefficient
Hyperbolic Systems --$tHyperbolicity of Quasilinear and
Nonlinear Systems --$tSolid Mechanics and Elastic Waves
--$tLagrangian Gas Dynamics and the p-System
--$tElectromagnetic Waves --$tCharacteristics and Riemann
Problems for Linear Hyperbolic Equations --$tSolution to the
Cauchy Problem --$tSuperposition of Waves and Characteristic
Variables --$tLeft Eigenvectors --$tSimple Waves
--$tAcoustics --$tDomain of Dependence and Range of
Influence --$tDiscontinuous Solutions --$tThe Riemann
Problem for a Linear System --$tThe Phase Plane for Systems
of Two Equations --$tCoupled Acoustics and Advection
--$tInitial--Boundary-Value Problems --$tFinite Volume
Methods --$tGeneral Formulation for Conservation Laws --$tA
Numerical Flux for the Diffusion Equation --$tNecessary
Components for Convergence --$tThe CFL Condition --$tAn
Unstable Flux --$tThe Lax--Friedrichs Method --$tThe
Richtmyer Two-Step Lax--Wendroff Method --$tUpwind Methods
--$tThe Upwind Method for Advection --$tGodunov's Method for
Linear Systems --$tThe Numerical Flux Function for Godunov's
Method --$tThe Wave-Propagation Form of Godunov's Method.
505 80 $tFlux-Difference vs. Flux-Vector Splitting
--$tRoe's Method --$tIntroduction to the Clawpack Software
--$tBasic Framework --$tObtaining Clawpack --$tUsing
Clawpack--a Guide through example1 --$tOther User-Supplied
Routines and Files --$tAuxiliary Arrays and setaux.f --$tAn
Acoustics Example --$tHigh-Resolution Methods --$tThe
Lax--Wendroff Method --$tThe Beam--Warming Method
--$tPreview of Limiters --$tThe REA Algorithm with Piecewise
Linear Reconstruction --$tChoice of Slopes --$tOscillations
--$tTotal Variation --$tTVD Methods Based on the REA
Algorithm --$tSlope-Limiter Methods --$tFlux Formulation
with Piecewise Linear Reconstruction --$tFlux Limiters
--$tTVD Limiters --$tHigh-Resolution Methods for Systems
--$tImplementation --$tExtension to Nonlinear Systems
--$tCapacity-Form Differencing --$tNonuniform Grids
--$tBoundary Conditions and Ghost Cells --$tPeriodic
Boundary Conditions --$tAdvection --$tAcoustics
--$tConvergence, Accuracy, and Stability --$tConvergence
--$tOne-Step and Local Truncation Errors --$tStability
Theory --$tAccuracy at Extrema --$tOrder of Accuracy Isn't
Everything --$tModified Equations --$tAccuracy Near
Discontinuities --$tVariable-Coefficient Linear Equations
--$tAdvection in a Pipe --$tFinite Volume Methods --$tThe
Color Equation --$tThe Conservative Advection Equation
--$tEdge Velocities --$tVariable-Coefficient Acoustics
Equations --$tConstant-Impedance Media --$tVariable
Impedance --$tSolving the Riemann Problem for Acoustics
--$tTransmission and Reflection Coefficients --$tGodunov's
Method --$tHigh-Resolution Methods --$tWave Limiters.
505 80 $tHomogenization of Rapidly Varying Coefficients
--$tOther Approaches to High Resolution --$tCentered-in-Time
Fluxes --$tHigher-Order High-Resolution Methods
--$tLimitations of the Lax-Wendroff (Taylor Series) Approach
--$tSemidiscrete Methods plus Time Stepping --$tStaggered
Grids and Central Schemes --$tNonlinear Equations
--$tNonlinear Scalar Conservation Laws --$tTraffic Flow
--$tQuasilinear Form and Characteristics --$tBurgers'
Equation --$tRarefaction Waves --$tCompression Waves
--$tVanishing Viscosity --$tEqual-Area Rule --$tShock Speed
--$tThe Rankine-Hugoniot Conditions for Systems
--$tSimilarity Solutions and Centered Rarefactions --$tWeak
Solutions --$tManipulating Conservation Laws
--$tNonuniqueness, Admissibility, and Entropy Conditions
--$tEntropy Functions --$tLong-Time Behavior and N-Wave
Decay --$tFinite Volume Methods for Nonlinear Scalar
Conservation Laws --$tGodunov's Method --$tFluctuations,
Waves, and Speeds --$tTransonic Rarefactions and an Entropy
Fix --$tNumerical Viscosity --$tThe Lax-Friedrichs and Local
Lax-Friedrichs Methods --$tThe Engquist-Osher Method
--$tE-schemes --$tHigh-Resolution TVD Methods --$tThe
Importance of Conservation Form --$tThe Lax-Wendroff Theorem
--$tThe Entropy Condition --$tNonlinear Stability
--$tNonlinear Systems of Conservation Laws --$tThe Shallow
Water Equations --$tDam-Break and Riemann Problems
--$tCharacteristic Structure --$tA Two-Shock Riemann
Solution --$tWeak Waves and the Linearized Problem
--$tStrategy for Solving the Riemann Problem --$tShock Waves
and Hugoniot Loci --$tSimple Waves and Rarefactions.
505 80 $tSolving the Dam-Break Problem --$tThe General
Riemann Solver for Shallow Water Equations --$tShock
Collision Problems --$tLinear Degeneracy and Contact
Discontinuities --$tGas Dynamics and the Euler Equations
--$tPressure --$tEnergy --$tThe Euler Equations
--$tPolytropic Ideal Gas --$tEntropy --$tIsothermal Flow
--$tThe Euler Equations in Primitive Variables --$tThe
Riemann Problem for the Euler Equations --$tContact
Discontinuities --$tRiemann Invariants --$tSolution to the
Riemann Problem --$tThe Structure of Rarefaction Waves
--$tShock Tubes and Riemann Problems --$tMultifluid Problems
--$tOther Equations of State and Incompressible Flow
--$tFinite Volume Methods for Nonlinear Systems
--$tGodunov's Method --$tConvergence of Godunov's Method
--$tApproximate Riemann Solvers --$tHigh-Resolution Methods
for Nonlinear Systems --$tAn Alternative Wave-Propagation
Implementation of Approximate Riemann Solvers
--$tSecond-Order Accuracy --$tFlux-Vector Splitting
--$tTotal Variation for Systems of Equations --$tSome
Nonclassical Hyperbolic Problems --$tNonconvex Flux
Functions --$tNonstrictly Hyperbolic Problems --$tLoss of
Hyperbolicity --$tSpatially Varying Flux Functions
--$tNonconservative Nonlinear Hyperbolic Equations
--$tNonconservative Transport Equations --$tSource Terms and
Balance Laws --$tFractional-Step Methods --$tAn
Advection-Reaction Equation --$tGeneral Formulation of
Fractional-Step Methods for Linear Problems --$tStrang
Splitting --$tAccuracy of Godunov and Strang Splittings
--$tChoice of ODE Solver.
505 80 $tImplicit Methods, Viscous Terms, and Higher-Order
Derivatives --$tSteady-State Solutions --$tBoundary
Conditions for Fractional-Step Methods --$tStiff and
Singular Source Terms --$tLinear Traffic Flow with On-Ramps
or Exits --$tRankine-Hugoniot Jump Conditions at a Singular
Source --$tNonlinear Traffic Flow with On-Ramps or Exits
--$tAccurate Solution of Quasisteady Problems --$tBurgers
Equation with a Stiff Source Term --$tNumerical Difficulties
with Stiff Source Terms --$tRelaxation Systems
--$tRelaxation Schemes --$tMultidimensional Problems
--$tMultidimensional Hyperbolic Problems --$tDerivation of
Conservation Laws --$tAdvection --$tCompressible Flow
--$tAcoustics --$tHyperbolicity --$tThree-Dimensional
Systems --$tShallow Water Equations --$tEuler Equations
--$tSymmetry and Reduction of Dimension --$tMultidimensional
Numerical Methods --$tFinite Difference Methods --$tFinite
Volume Methods and Approaches to Discretization --$tFully
Discrete Flux-Differencing Methods --$tSemidiscrete Methods
with Runge-Kutta Time Stepping --$tDimensional Splitting
--$tMultidimensional Scalar Equations --$tThe Donor-Cell
Upwind Method for Advection --$tThe Corner-Transport Upwind
Method for Advection --$tWave-Propagation Implementation of
the CTU Method --$tvon Neumann Stability Analysis --$tThe
CTU Method for Variable-Coefficient Advection
--$tHigh-Resolution Correction Terms --$tRelation to the
Lax-Wendroff Method --$tDivergence-Free Velocity Fields
--$tNonlinear Scalar Conservation Laws --$tConvergence
--$tMultidimensional Systems --$tConstant-Coefficient Linear
Systems.
505 80 $tThe Wave-Propagation Approach to Accumulating
Fluxes --$tCLAWPACK Implementation --$tAcoustics
--$tAcoustics in Heterogeneous Media --$tTransverse Riemann
Solvers for Nonlinear Systems --$tShallow Water Equations
--$tBoundary Conditions --$tElastic Waves --$tDerivation of
the Elasticity Equations --$tThe Plane-Strain Equations of
Two-Dimensional Elasticity --$tOne-Dimensional Slices
--$tBoundary Conditions --$tThe Plane-Stress Equations and
Two-Dimensional Plates --$tA One-Dimensional Rod
--$tTwo-Dimensional Elasticity in Heterogeneous Media
--$tFinite Volume Methods on Quadrilateral Grids --$tCell
Averages and Interface Fluxes --$tLogically Rectangular
Grids --$tGodunov's Method --$tFluctuation Form
--$tAdvection Equations --$tAcoustics --$tShallow Water and
Euler Equations --$tUsing CLAWPACK on Quadrilateral Grids
--$tBoundary Conditions.
650 0 $aDifferential equations, Hyperbolic$xNumerical
solutions.
650 0 $aFinite volume method.
650 0 $aConservation laws (Mathematics)
856 42 $3Publisher
description$uhttp://www.loc.gov/catdir/description/cam022/20
01052642.html
856 41 $3Table of contents$uhttp://www.loc.gov/catdir/toc/
cam024/2001052642.html
994 $aE0$bIPL
