Fluid dynamics: theoretical and computational approaches

摘要: Important Nomenclature Kinematics of Fluid Motion Introduction to Continuum Particles Inertial Coordinate Frames a The Time Derivatives Velocity and Acceleration Steady Nonsteady Flow Trajectories Streamlines Material Volume Surface Relation between Elemental Volumes Kinematic Formulas Euler Reynolds Control Deformation Vorticity Circulation References Problems Conservation Laws the Kinetics Density Mass Principle Using Linear Angular Momentum Equations Energy General Closure Problem Stokes' Law Friction Interpretation Pressure Dissipation Function Constitutive Equation for Non-Newtonian Fluids Thermodynamic Aspects Viscosity in Lagrangian Coordinates Navier--Stokes Formulation Viscous Compressible Incompressible Inviscid (Euler's Equations) Initial Boundary Conditions Mathematical Nature Some Results Based on Nondimensional Parameters Transformation Stream Surfaces Form Part I: Bernoulli Constant Method Conformal Mapping Flows Sources, Sinks, Doublets Three Dimensions II: Basic Thermodynamics Subsonic Supersonic Critical Stagnation Quantities Isentropic Ideal Gas Relations Unsteady One-dimension Plane Gases Theory Shock Waves Laminar Exact Solutions Slow Layers Layer 2-D Curved Separation Transformed Integral Free Numerical Solution Three-Dimensional Attachment Bodies Revolution Yawed Cylinders Point On Rotating Blades 3-D Second-Order Inverse III: Hyperbolic Grid Generation Algorithms Thin-Layer (TLNS) Turbulent Stability Statistical Description Turbulence Plane-Parallel Temporal at In nite Number Algorithm Orr--Sommerfeld Transition Methods Mechanics Concepts Internal Structure Physical Space Wave-Number Universal Equilibrium Development Averaged Empirical Prandtl's Mixing-Length Hypothesis Wall-Bound Analysis Pro les Differential IV: Modeling Generalization Boussinesq's Zero-Equation Shear One-Equation Two-Equation (K-Ae) Reynolds' Stress Application Thin Algebraic A Nonlinear Current Approaches Heuristic Illustrative Instability Large Eddy Simulation Exposition 1: Base Vectors Various Representations Rectangular Cartesian Systems Scalars, Vectors, Tensors Operations Multiplication Tensor Vector Scalar Two Collection Usable Taylor Expansion Principal Axes T Quadratic Eigenvalue Representation Curvilinear Christoffel Symbols Derivative Double Dot Products 2: Theorems Gauss, Green, Stokes Gauss' Theorem Green's 3: Geometry Curves 4: Scalars 5: Potential Green An First Formula 6: Singularities First-Order ODEs Their Classi cation 7: De nitions Gauss Weingarten Normal Geodesic Curvatures 8: Finite Difference Approximation Applied PDEs Calculus Differences Iterative Root Finding Integration Approximations Partial Parabolic Elliptic 9: Frame Invariancy Orthogonal Arbitrary Reference Check Use Q Expositions Index