Introduction to Theoretical and Computational Fluid Dynamics

Chapter 1: Kinematics of a Flow 1.1: Fluid velocity and motion of fluid parcels 1.2: Lagrangian labels 1.3: Properties of parcels, conservation of mass, and the continuity equation 1.4: Material lines, material vectors, and material surfaces 1.5: Differential geometry of surfaces 1.6: Description of a material surface in Eulerian form 1.7: Streamlines, stream tubes, path lines, and streak lines 1.8: Vorticity, vortex lines, vortex tubes, and circulation around loops 1.9: Line vortices and vortex sheets Chapter 2: Analysis of Kinematics 2.1: Irrotational flows and the velocity potential 2.2: The reciprocal relation for harmonic functions, and Green's functions of Laplace's equation 2.3: Integral representation and further properties of potential flow 2.4: The vector potential for incompressible flow 2.5: Representation of an incompressible flow in terms in the vorticity 2.6: Representation of a flow in terms of the rate of expansion and vorticity 2.7: Stream functions for incompressible flow 2.8: Flow induced by vorticity 2.9: Axisymmetric flow induced by vorticity 2.10: Two-dimensional flow induced by vorticity Chapter 3: Stresses, the Equation of Motion, and the Vorticity Transport Equation 3.1: Forces acting in a fluid, traction, the stress tensor, and the equation of motion 3.2: Constitutive relations for the stress tensor 3.3: Traction, force, torque, energy dissipation, and the reciprocal theorem for incompressible Newtonian fluids 3.4: Navier-Stokes', Euler's and Bernoulli's equation 3.5: Equations and boundary conditions governing the motion of an incompressible Newtonian fluid 3.6: Traction, vorticity, and flow kinematics on rigid boundaries, free surfaces, and fluid interfaces 3.7: Scaling of the Navier-Stokes equation and dynamic similtude 3.8: Evolution of circulation around material loops and dynamics of the vorticity field 3.9: Computation of exact solutions to the equation of motion in two dimensions based in the vorticity transport equation Chapter 4: Hydrostatics 4.1: Pressure distribution within a fluid in rigid body motion 4.2: The Laplace-Young equation 4.3: Two-dimensional interfaces 4.4: Axisymmetric interfaces 4.5: Three-dimensional interfaces Chapter 5: Computing Incompressible Flows 5.1: Steady unidirectional flows 5.2: Unsteady unidirectional flows 5.3: Stagnation-point flows 5.4: Flow due to a rotating disk 5.5: Flow in a corner due to a point source 5.6: Flow due to a point force Chapter 6: Flow at Low Reynolds Numbers 6.1: Equations and fundamental properties of Stokes flow 6.2: Local solutions in corners 6.3: Nearly-unidirectional flows 6.4: Flow due to a point force 6.5: Fundamental solutions of Stokes flow 6.6: Stokes flow past or due to the motion of rigid bodies and liquid drops 6.7: Computation of singularity representations 6.8: The Lorentz reciprocal theorem and its applications 6.9: Boundary integral representation of Stokes flows 6.10: Boundary-integral-equation methods 6.11: Generalized Faxen's relations 6.12: Formulation of two-dimensional Stokes flow in complex variables 6.13: Effects of inertia and Oseen flow 6.14: Unsteady Stokes flow 6.15: Computation of unsteady Stokes flow past or due to the motion of particles Chapter 7: Irrotational Flow 7.1: Equations and computation of irrotational flow 7.2: Flow past or due to the motion of three-dimensional body 7.3: Force and torque exerted on a three-dimensional body 7.4: Flow past or due to the motion of a sphere 7.5: Flow past or due to the motion of non-spherical bodies 7.6: Flow past of due to the motion of two-dimensional bodies 7.7: Computation of two-dimensional flow past or due to the motion of a body 7.8: Formulation of two-dimensional flow in complex variables 7.9: Conformal mapping 7.10: Applications of conformal mapping to flow past two-dimesensional bodies 7.11: The Schwarz-Christoffel transformation and its applications Chapter 8: Boundary Layers 8.1: Boundary-layer theory 8.2: The boundary layer on a semi-infinite flat plate 8.3: Boundary layers in acclerating and decelerating flow 8.4: Computation of boundary layers around two-dimensional bodies 8.5: Boundary layers in axisymmetric and three-dimensional flows 8.6: Unsteady boundary layers Chapter 9: Hydrodynamic Stability 9.1: Evolution equations and forumulation of the linear stability problem 9.2: Solution of the initial-value problem and normal-mode analysis 9.3: Normal-mode analysisof unidirectional flows 9.4: General theorems of the temporal stability of inviscid shear flows 9.5: Stability of a uniform layer subject to spatially periodic disturbances 9.6: Numerical solution of the Orr-Sommerfeld and Rayleigh equations 9.7: Stability of certain classes of unidirectional flows 9.8: Stability of a planar interface in potential flow 9.9: Viscous interfacial flows 9.10: Capillary instability of a curved interface 9.11: Inertial instability of rotating fluids Chapter 10: Boundary-Integral Methods for Potential Flow 10.1: The boundary-integral equation 10.2: Boundary-element methods 10.3: Generalized boundary-integral representations 10.4: The single-layer potential 10.5: The double-layer potential 10.6: Investigation of integral equations of the second kind 10.7: Regularization of integral equations of the second kind 10.8: Completed double-layer representation for exterior flow 10.9: Iterative solution of integral equations of the second kind Chapter 11: Vortex Motion 11.1: Invariants of the motion 11.2: Point vortices 11.3: Vortex blobs 11.4: Two-dimensional vortex sheets 11.5: Two-dimensional flows with distributed vorticity 11.6: Two-dimensional vortex patches 11.7: Axisymmetric flow 11.8: Three-dimensional flow Chapter 12: Finite-Difference Methods for the Convection-Diffusion Equation 12.1: Definitions and procedures 12.2: One-dimensional diffusion 12.3: Diffusion in two and three dimensions 12.4: One-dimensional convection 12.5: Convection in two and three dimensions 12.6: Convection-diffusion in one dimension 12.7: Convection-diffusion in two and three dimensions Chapter 13: Finite-Difference Methods for Incompressible Newtonian Flow 13.1: Methods based on the vorticity transport equation 13.2: Velocity-pressure formulation 13.3: Implementation of methods in primitive variables 13.4: Operator splitting, projection, and pressure-correction methods 13.5: Methods of modified dynamics or false transients Appendix A: Index Notation, Differential Operators, and Theorems of Vector Calculus A.1: Index Notation A.2: Vector and matrix products, differential operators in Cartesian coordinates A.3: Orthogonal curvilinear coordinates A.4: Differential operators in cylindrical and plane polar coordinates A.5: Differential operators in spherical polar coordinates A.6: Integral theorems of vector calculus Appendix B: Primer of Numerical Methods B.1: Linear algebra equations B.2: Computation of eigenvalues B.3: Nonlinear algebraic equations B.4: Function interpolation B.5: Computation of derivatives B.6: Function integration B.7: Function approximation B.8: Integration of ordinary differential equations B.9: Computation of special functions