Sinossi
1. Computational Fluid Dynamics: An Introduction.- 1.1 Advantages of Computational Fluid Dynamics.- 1.2 Typical Practical Problems.- 1.2.1 Complex Geometry, Simple Physics.- 1.2.2 Simpler Geometry, More Complex Physics.- 1.2.3 Simple Geometry, Complex Physics.- 1.3 Equation Structure.- 1.4 Overview of Computational Fluid Dynamics.- 1.5 Further Reading.- 2. Partial Differential Equations.- 2.1 Background.- 2.1.1 Nature of a Well-Posed Problem.- 2.1.2 Boundary and Initial Conditions.- 2.1.3 Classification by Characteristics.- 2.1.4 Systems of Equations.- 2.1.5 Classification by Fourier Analysis.- 2.2 Hyperbolic Partial Differential Equations.- 2.2.1 Interpretation by Characteristics.- 2.2.2 Interpretation on a Physical Basis.- 2.2.3 Appropriate Boundary (and Initial) Conditions.- 2.3 Parabolic Partial Differential Equations.- 2.3.1 Interpretation by Characteristics.- 2.3.2 Interpretation on a Physical Basis.- 2.3.3 Appropriate Boundary (and Initial) Conditions.- 2.4 Elliptic Partial Differential Equations.- 2.4.1 Interpretation by Characteristics.- 2.4.2 Interpretation on a Physical Basis.- 2.4.3 Appropriate Boundary Conditions.- 2.5 Traditional Solution Methods.- 2.5.1 The Method of Characteristics.- 2.5.2 Separation of Variables.- 2.5.3 Green's Function Method.- 2.6 Closure.- 2.7 Problems.- 3. Preliminary Computational Techniques.- 3.1 Discretisation.- 3.1.1 Converting Derivatives to Discrete Algebraic Expressions.- 3.1.2 Spatial Derivatives.- 3.1.3 Time Derivatives.- 3.2 Approximation to Derivatives.- 3.2.1 Taylor Series Expansion.- 3.2.2 General Technique.- 3.2.3 Three-point Asymmetric Formula for % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaWadaWdaeaapeGaamizaiqadsfagaqeaiaac+cacaWGKbGaamiE % aaGaay5waiaaw2faa8aadaqhaaWcbaWdbiaadQgaa8aabaWdbiaad6 % gaaaaaaa!3EE5! $$ \left[ {d\bar T/dx} \right]_j^n $$.- 3.3 Accuracy of the Discretisation Process.- 3.3.1 Higher-Order vs Low-Order Formulae.- 3.4 Wave Representation.- 3.4.1 Significance of Grid Coarseness.- 3.4.2 Accuracy of Representing Waves.- 3.4.3 Accuracy of Higher-Order Formulae.- 3.5 Finite Difference Method.- 3.5.1 Conceptual Implementation.- 3.5.2 DIFF: Transient Heat Conduction (Diffusion) Problem.- 3.6 Closure.- 3.7 Problems.- 4. Theoretical Background.- 4.1 Convergence.- 4.1.1 Lax Equivalence Theorem.- 4.1.2 Numerical Convergence.- 4.2 Consistency.- 4.2.1 FTCS scheme.- 4.2.2 Fully Implicit Scheme.- 4.3 Stability.- 4.3.1 Matrix Method: FTCS Scheme.- 4.3.2 Matrix Method: General Two-Level Scheme.- 4.3.3 Matrix Method: Derivative Boundary Conditions.- 4.3.4 Von Neumann Method: FTCS Scheme.- 4.3.5 Von Neumann Method: General Two-Level Scheme.- 4.4 Solution Accuracy.- 4.4.1 Richardson Extrapolation.- 4.5 Computational Efficiency.- 4.5.1 Operation Count Estimates.- 4.6 Closure.- 4.7 Problems.- 5. Weighted Residual Methods.- 5.1 General Formulation.- 5.1.1 Application to an Ordinary Differential Equation.- 5.2 Finite Volume Method.- 5.2.1 Equations with First Derivatives Only.- 5.2.2 Equations with Second Derivatives.- 5.2.3 FIVOL: Finite Volume Method Applied to Laplace's Equation.- 5.3 Finite Element Method and Interpolation.- 5.3.1 Linear Interpolation.- 5.3.2 Quadratic Interpolation.- 5.3.3 Two-Dimensional Interpolation.- 5.4 Finite Element Method and the Sturm-Liouville Equation.- 5.4.1 Detailed Formulation.- 5.4.2 STURM: Computation of the Sturm Liouville Equation.- 5.5 Further Applications of the Finite Element Method.- 5.5.1 Diffusion Equation.- 5.5.2 DUCT: Viscous Flow in a Rectangular Duct.- 5.5.3 Distorted Computational Domains: Isoparametric Formulation.- 5.6 Spectral Method.- 5.6.1 Diffusion Equation.- 5.6.2 Neumann Boundary Conditions.- 5.6.3 Pseudospectral Method.- 5.7 Closure.- 5.8 Problems
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