LEADER 07882cam a2200397 i 4500001 99125428121306421 005 20240502065520.0 008 210527s2021 nyua b 001 0 eng c 020 9781071613429 |qhardcover 020 1071613421 |qhardcover 020 |z9781071613443 |qeBook 035 (OCoLC)on1255873527 040 UKMGB |beng |erda |cUKMGB |dOCLCO |dOCLCF |dVA@ |dOCLCO |dOHX |dEAU |dPAU |dSTF 042 pcc 050 4 QA1 |b.A647 v.118 2021 082 04 533.2015153535 |223 100 1 Godlewski, Edwige, |eauthor. 245 10 Numerical approximation of hyperbolic systems of conservation laws / |cEdwige Godlewski, Pierre-Arnaud Raviart. 250 Second edition. 264 1 New York : |bSpringer, |c[2021] 300 xiii, 840 pages : |billustrations ; |c24 cm. 336 text |btxt |2rdacontent 337 unmediated |bn |2rdamedia 338 volume |bnc |2rdacarrier 490 1 Applied mathematical sciences, |x0066-5452 ; |v118 504 Includes bibliographical references (pages 749-829) and index. 505 00 |gIntroduction -- |tDefinitions and Examples -- |tFluid Systems in Eulerian and Lagrangian Frames -- |tSome Averaged Models : Shallow Water, Flow in a Duct, and Two-Phase Flow -- |tWeak Solutions of Systems of Conservation Laws -- |tCharacteristics in the Scalar One-Dimensional Case -- |tWeak Solutions : The Rankine-Hugoniot Condition -- |tExample of Nonuniqueness of Weak Solutions -- |tEntropy Solution -- |tA Mathematical Notion of Entropy -- |tThe Vanishing Viscosity Method -- |tExistence and Uniqueness of the Entropy Solution in the Scalar Case -- |tNotes -- |tNonlinear Hyperbolic Systems in One Space Dimension -- |tLinear Hyperbolic Systems with Constant Coefficients -- |tThe Nonlinear Case, Definitions and Examples -- |tChange of Variables, Change of Frame -- |tThe Gas Dynamics Equations -- |tIdeal MHD -- |tSimple Waves and Riemann Invariants -- |tRarefaction Waves -- |tRiemann Invariants -- |tShock Waves and Contact Discontinuities |tCharacteristic Curves and Entropy Conditions -- |tCharacteristic Curves -- |tThe Lax Entropy Conditions -- |tOther Entropy Conditions -- |tSolution of the Riemann Problem -- |tExamples of Systems of Two Equations -- |tThe Case of a Linear or a Linearly Degenerate System -- |tThe Riemann Problem for the p-System -- |tThe Riemann Problem for the Barotropic Euler System -- |tNotes -- |tGas Dynamics and Reacting Flows -- |tPreliminaries -- |tProperties of the Physical Entropy -- |tIdeal Gases -- |tEntropy Satisfying Shock Conditions -- |tSolution of the Riemann Problem -- |tReacting Flows : The Chapman-Jouguet Theory -- |tReacting Flows : The Z.N.D. Model for Detonations -- |tNotes -- |tFinite Volume Schemes for One-Dimensional Systems -- |tGeneralities on Finite Volume Methods for Systems -- |tExtension of Scalar Schemes to Systems : Some Examples -- |tL² Stability -- |tDissipation and Dispersion -- |tGodunov's Method -- |tGodunov's Method for Systems |tThe Gas Dynamics Equations in a Moving Frame -- |tGodunov's Method in Lagrangian Coordinates -- |tGodunov's Method in Eulerian Coordinates (Direct Method) -- |tGodunov's Method in Eulerian Coordinates (Lagrangian Step + Projection) -- |tGodunov's Method in a Moving Grid -- |tGodunov-Type Methods -- |tApproximate Riemann Solvers and Godunov-Type Methods -- |tRoe's Method and Variants -- |tThe H.L.L. Method -- |tOsher's Scheme -- |tRoe-Type Methods for the Gas Dynamics System -- |tRoe's Method for the Gas Dynamics Equations : (I) The Ideal Gas Case -- |tRoe's Method for the Gas Dynamics Equations : (II) The "Real Gas" Case -- |tA Roe-Type Linearization Based on Shock Curve Decomposition -- |tAnother Roe-Type Linearization Associated with a Path -- |tThe Case of the Gas Dynamics System in Lagrangian Coordinates -- |tFlux Vector Splitting Methods -- |tGeneral Formulation -- |tApplication to the Gas Dynamics Equations : (I) Steger and Warming's Approach-- |tApplication to the Gas Dynamics Equations : (II) Van Leer's Approach -- |tVan Leer's Second-Order Method -- |tVan Leer's Method for Systems -- |tSolution of the Generalized Riemann Problem -- |tThe G.R.P. for the Gas Dynamics Equations in Lagrangian Coordinates -- |tUse of the G.R.P. in van Leer's Method -- |tKinetic Schemes for the Euler Equations -- |tThe Boltzmann Equation -- |tThe B.G.K. Model -- |tThe Kinetic Scheme -- |tSome Extensions of the Kinetic Approach -- |tRelaxation Schemes -- |tIntroduction to Relaxation -- |tModel Examples -- |tA Relaxation Scheme for the Euler System -- |tNotes -- |tThe Case of Multidimensional Systems -- |tGeneralities on Multidimensional Hyperbolic Systems -- |tDefinitions -- |tCharacteristics -- |tSimple Plane Waves -- |tShock Waves -- |tThe Gas Dynamics Equations in Two Space Dimensions -- |tEntropy and Entropy Variables -- |tInvariance of the Euler Equations -- |tEigenvalues -- |tCharacteristics's Approach-- |tPlane Wave Solutions : Self-Similar Solutions -- |tMultidimensional Finite Difference Schemes -- |tDirect Approach -- |tDimensional Splitting -- |tFinite-Volume Methods -- |tDefinition of the Finite-Volume Method -- |tGeneral Results -- |tUsual Schemes -- |tSecond-Order Finite-Volume Schemes -- |tMuscl-Type Schemes -- |tOther Approaches -- |tAn Introduction to All-Mach Schemes for the System of Gas Dynamics -- |tThe Low Mach Limit of the System of Gas Dynamics -- |tAsymptotic Analysis of the Semi-Discrete Roe Scheme -- |tAn All-Mach Semi-Discrete Roe Scheme -- |tAsymptotic Analysis of the Semi-Discrete HLL Scheme -- |tAn All-Mach Semi-Discrete HLL Scheme -- |tNotes -- |tAn Introduction to Boundary Conditions -- |tThe Initial Boundary Value Problem in the Linear Case -- |tScalar Advection Equations -- |tOne-Dimensional Linear Systems : Linearization -- |tMultidimensional Linear Systems -- |tThe Nonlinear Approach -- |tNonlinear Equations -- |tNonlinear Systems -- |tGas Dynamics |tFluid Boundary (Linearized Approach) -- |tSolid or Rigid Wall Boundary -- |tAbsorbing Boundary Conditions -- |tNumerical Treatment -- |tFinite Difference Schemes -- |tFinite Volume Approach -- |tNotes -- |tSource Terms -- |tIntroduction to Source Terms -- |tSome General Considerations for Systems with Source Terms -- |tSimple Examples of Source Terms in the Scalar Case -- |tNumerical Treatment of Source Terms -- |tExamples of Systems with Source Terms -- |tSystems with Geometric Source Terms -- |tNonconservative Systems -- |tStationary Waves and Resonance -- |tCase of a Nozzle with Discontinuous Section -- |tThe Example of the Shallow Water System -- |tSpecific Numerical Treatment of Source Terms -- |tSome Numerical Considerations for Flow in a Nozzle -- |tPreserving Equilibria, Well-Balanced Schemes -- |tSchemes for the Shallow Water System -- |tSimple Approximate Riemann Solvers -- |tDefinition of Simple Approximate Riemann Solvers -- |tWell-Balanced Simple Schemesynamics |tSimple Approximate Riemann Solvers in Lagrangian or Eulerian Coordinates -- |tThe Example of the Gas Dynamics Equations with Gravity and Friction -- |tLink with Relaxation Schemes -- |tStiff Source Terms, Asymptotic Preserving Numerical Schemes -- |gIntroduction -- |tSome Simple Examples -- |tDerivation of an AP Scheme for the Linear Model -- |tEuler System with Gravity and Friction -- |tInterface Coupling -- |tIntroduction to Interface Coupling -- |tThe Interface Coupling Condition -- |tNumerical Coupling -- |tNotes -- |gReferences -- |gIndex. 650 0 Gas dynamics. 650 0 Conservation laws (Mathematics) 650 0 Differential equations, Hyperbolic |xNumerical solutions. 650 7 Conservation laws (Mathematics) |2fast |0(OCoLC)fst00875496 650 7 Differential equations, Hyperbolic |xNumerical solutions. |2fast |0(OCoLC)fst00893465 650 7 Gas dynamics. |2fast |0(OCoLC)fst00938238 700 1 Raviart, Pierre-Arnaud, |d1939- |eauthor. 830 0 Applied mathematical sciences (Springer-Verlag New York Inc.) ; |v118. 914 (OCoLC)on1255873527 |bOCoLC |cmatch |d20240501 |eprocessed |f1255873527