| Description |
1 online resource (385 p.) |
| Contents |
Intro -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- Author biography -- 1. Essence of Fluid Dynamics -- 1.1 Introduction -- 1.2 General Form of Transport Equations -- 1.2.1 Derivation of General Form of Transport Equations -- 1.2.2 Maximum Principle, Conservativeness, and Boundedness -- 1.3 Navier-Stokes Equations -- 1.3.1 Continuity Equation and Momentum Equations -- 1.3.2 Dimensionless Form of Equations and Reynolds Number -- Note -- 2. Finite Difference and Finite Volume Methods -- 2.1 Finite Difference Method -- 2.1.1 Finite Differences |
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2.1.2 Example: Laminar Channel Flow -- 2.1.3 TDMA Algorithm -- 2.2 Finite Volume Method -- 2.3 Error Analysis -- 2.3.1 Bounded Scheme and Positive Scheme -- 2.3.2 Properties of Positive Scheme -- 2.3.3 Global Error and Truncation Error -- 2.3.4 Global Error Estimation -- 2.4 Finite Volume Method (Continued) -- 2.4.1 Virtual Control Volume and Virtual Node -- 2.4.2 Example: Channel Flow Consisting of Two Immiscible Fluids -- 2.5 A Glimpse of Turbulence -- 2.5.1 Introduction -- 2.5.2 Mixing Length Model -- 2.5.3 Example: Turbulent Channel Flow -- 2.6 The CFD Procedure -- Notes |
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3. Numerical Schemes -- 3.1 Schemes for Time Advancing -- 3.1.1 Example: Start-Up of Couette Flow -- 3.1.2 Euler Explicit Scheme -- 3.1.3 Consistency, Stability, and Convergence -- 3.1.4 von Neumann and Matrix Stability Analysis Methods -- 3.1.5 Euler Implicit Scheme -- 3.1.6 Crank-Nicolson Scheme -- 3.1.7 Runge-Kutta Schemes -- 3.1.8 Second-Order Backward Difference and Adams-Bashforth Schemes -- 3.2 Unsteady Convection-Diffusion Equation -- 3.2.1 Example: Mass Transfer in 1-D Flow -- 3.2.2 FTCS Scheme -- 3.2.3 Local Mesh Refinement -- 3.3 Schemes for Convection Term |
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3.3.1 First-Order Upwind Scheme -- 3.3.2 Godunov Theorem -- 3.3.3 Second- and Higher-Order Upwind Schemes -- 3.3.4 Deferred-Correction Approach -- 3.3.5 Hybrid Schemes -- 3.3.6 Bounded Second-Order Schemes -- 3.3.7 ENO and WENO Schemes -- 3.3.8 Harten's Lemma -- 3.4 Proper Boundary Conditions -- Notes -- 4. Numerical Algorithms -- 4.1 Introduction -- 4.2 Basic Iterative Methods -- 4.2.1 Jacobi and Gauss-Seidel Iteration Methods -- 4.2.2 Successive Over-Relaxation (SOR) Method -- 4.2.3 Alternating Direction Implicit (ADI) Method -- 4.2.4 Strongly Implicit Procedure (SIP) Method |
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4.3 Krylov Subspace Methods -- 4.3.1 Conjugate Gradient Method -- 4.3.2 Condition Number and Preconditioned Conjugate Gradient Method -- 4.3.3 GMRES, BiCGSTAB, and '\' -- 4.4 FFT Method -- 5. Navier-Stokes Solution Methods -- 5.1 Odd-Even Decoupling -- 5.1.1 Example: 1-D Flow Through Filter -- 5.1.2 Staggered Mesh -- 5.2 Navier-Stokes Solution Methods -- 5.2.1 Coupled vs. Segregated Methods -- 5.2.2 SIMPLE Method -- 5.2.3 Projection Method -- 5.2.4 Co-located Mesh and Momentum Interpolation Method -- 5.3 Example: Lid-Driven Cavity Flow -- 5.3.1 Problem Statement, Mesh, and Formulas |
| Notes |
Description based upon print version of record |
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5.3.2 Under-Relaxation |
| Subject |
Computational fluid dynamics.
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Computational fluid dynamics
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| Form |
Electronic book
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| ISBN |
9781000463224 |
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1000463222 |
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