LEADER 04861nam 2200625Ia 450 001 9910139752503321 005 20170809163044.0 010 $a1-282-68766-2 010 $a9786612687662 010 $a3-527-62796-0 010 $a3-527-62797-9 035 $a(CKB)1000000000790290 035 $a(EBL)481810 035 $a(OCoLC)441875099 035 $a(SSID)ssj0000340207 035 $a(PQKBManifestationID)11248267 035 $a(PQKBTitleCode)TC0000340207 035 $a(PQKBWorkID)10364862 035 $a(PQKB)11580238 035 $a(MiAaPQ)EBC481810 035 $a(PPN)140606009 035 $a(EXLCZ)991000000000790290 100 $a20081030d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical models of fluid dynamics$b[electronic resource] $emodeling, theory, basic numerical facts : an introduction /$fRainer Ansorge and Thomas Sonar 205 $a2nd ed. 210 $aWeinheim $cWiley-VCH ;$a[Chichester $cJohn Wiley distributor]$dc2009 215 $a1 online resource (245 p.) 300 $aDescription based upon print version of record. 311 $a3-527-40774-X 320 $aIncludes bibliographical references ( p. 227) and index. 327 $aMathematical Models of Fluid Dynamics; Contents; Preface to the Second Edition; Preface to the First Edition; 1 Ideal Fluids; 1.1 Modeling by Euler's Equations; 1.2 Characteristics and Singularities; 1.3 Potential Flows and (Dynamic) Buoyancy; 1.4 Motionless Fluids and Sound Propagation; 2 Weak Solutions of Conservation Laws; 2.1 Generalization of What Will Be Called a Solution; 2.2 Traffic Flow Example with Loss of Uniqueness; 2.3 The Rankine-Hugoniot Condition; 3 Entropy Conditions; 3.1 Entropy in the Case of an Ideal Fluid; 3.2 Generalization of the Entropy Condition 327 $a3.3 Uniqueness of Entropy Solutions3.4 Kruzkov's Ansatz; 4 The Riemann Problem; 4.1 Numerical Importance of the Riemann Problem; 4.2 The Riemann Problem for Linear Systems; 4.3 The Aw-Rascle Traffic Flow Model; 5 Real Fluids; 5.1 The Navier-Stokes Equations Model; 5.2 Drag Force and the Hagen-Poiseuille Law; 5.3 Stokes Approximation and Artificial Time; 5.4 Foundations of the Boundary Layer Theory and Flow Separation; 5.5 Stability of Laminar Flows; 5.6 Heated Real Gas Flows; 5.7 Tunnel Fires; 6 Proving the Existence of Entropy Solutions by Discretization Procedures 327 $a6.1 Some Historical Remarks6.2 Reduction to Properties of Operator Sequences; 6.3 Convergence Theorems; 6.4 Example; 7 Types of Discretization Principles; 7.1 Some General Remarks; 7.2 Finite Difference Calculus; 7.3 The CFL Condition; 7.4 Lax-Richtmyer Theory; 7.5 The von Neumann Stability Criterion; 7.6 The Modified Equation; 7.7 Difference Schemes in Conservation Form; 7.8 The Finite Volume Method on Unstructured Grids; 7.9 Continuous Convergence of Relations; 8 A Closer Look at Discrete Models; 8.1 The Viscosity Form; 8.2 The Incremental Form; 8.3 Relations 327 $a8.4 Godunov Is Just Good Enough8.5 The Lax-Friedrichs Scheme; 8.6 A Glimpse of Gas Dynamics; 8.7 Elementary Waves; 8.8 The Complete Solution to the Riemann Problem; 8.9 The Godunov Scheme in Gas Dynamics; 9 Discrete Models on Curvilinear Grids; 9.1 Mappings; 9.2 Transformation Relations; 9.3 Metric Tensors; 9.4 Transforming Conservation Laws; 9.5 Good Practice; 9.6 Remarks Concerning Adaptation; 10 Finite Volume Models; 10.1 Difference Methods on Unstructured Grids; 10.2 Order of Accuracy and Basic Discretization; 10.3 Higher-Order Finite Volume Schemes; 10.4 Polynomial Recovery 327 $a10.5 Remarks Concerning Non-polynomial Recovery10.6 Remarks Concerning Grid Generation; Index; Suggested Reading 330 $aWithout sacrificing scientific strictness, this introduction to the field guides readers through mathematical modeling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behavior of the dynamics of physical flow. The book is carefully divided into three main parts: - The design of mathematical models of physical fluid flow;- A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as 606 $aFluid dynamics$xMathematical models 606 $aFluid mechanics 615 0$aFluid dynamics$xMathematical models. 615 0$aFluid mechanics. 676 $a532.5015118 700 $aAnsorge$b R$g(Rainer),$f1931-$0294988 701 $aSonar$b Th$g(Thomas)$0767915 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139752503321 996 $aMathematical models of fluid dynamics$91909538 997 $aUNINA