Introduction to theoretical and computational fluid dynamics /
This book discusses the fundamental principles and equations governing the motion of incompressible Newtonian fluids, and simultaneously introduces analytical and numerical methods for solving a broad range of pertinent problems. Topics include an in-depth discussion of kinematics, elements of diffe...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York :
Oxford University Press,
2011.
|
| Edition: | 2nd ed. |
| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- Cover; Contents; Preface; Preface to the Second Edition; Note to the Instructor; Note to the Reader; 1 Kinematic structure of a flow; 1.1 Fluid velocity and motion of fluid parcels; 1.1.1 Subparcels and point particles; 1.1.2 Velocity gradient; 1.1.3 Dyadic base; 1.1.4 Fundamental decomposition of the velocity gradient; 1.1.5 Vorticity; 1.1.6 Fluid parcel motion; 1.1.7 Irrotational and rotational flows; 1.1.8 Cartesian tensors; 1.2 Curvilinear coordinates; 1.2.1 Orthogonal curvilinear coordinates; 1.2.2 Cylindrical polar coordinates; 1.2.3 Spherical polar coordinates.
- 1.2.4 Plane polar coordinates1.2.5 Axisymmetric flow; 1.2.6 Swirling flow; 1.2.7 Nonorthogonal curvilinear coordinates; 1.3 Lagrangian labels of point particles; 1.3.1 The material derivative; 1.3.2 Point-particle acceleration; 1.3.3 Lagrangian mapping; 1.3.4 Deformation gradient; 1.4 Properties of fluid parcels and mass conservation; 1.4.1 Rate of change of parcel volume and Euler's theorem in kinematics; 1.4.2 Reynolds transport theorem; 1.4.3 Mass conservation and the continuity equation; 1.4.4 Incompressible fluids and solenoidal velocity fields; 1.4.5 Rate of change of parcel properties.
- 1.5 Point-particle motion1.5.1 Cylindrical polar coordinates; 1.5.2 Spherical polar coordinates; 1.5.3 Plane polar coordinates; 1.5.4 Particle rotation around an axis; 1.6 Material vectors and material lines; 1.6.1 Material vectors; 1.6.2 Material lines; 1.6.3 Frenet-Serret relations; 1.6.4 Evolution equations for a material line; 1.7 Material surfaces; 1.7.1 Tangential vectors and metric coefficients; 1.7.2 Normal vector and surface metric; 1.7.3 Evolution equations; 1.7.4 Flow rate of a vector field through a material surface; 1.8 Diffierential geometry of surfaces.
- 1.8.1 Metric tensor and the first fundamental form of a surface1.8.2 Second fundamental form of a surface; 1.8.3 Curvatures; 1.8.4 Curvature of a line in a plane; 1.8.5 Mean curvature of a surface as the divergence of the normal vector; 1.8.6 Mean curvature as a contour integral; 1.8.7 Curvature of an axisymmetric surface; 1.9 Interfacial surfactant transport; 1.9.1 Two-dimensional interfaces; 1.9.2 Axisymmetric interfaces; 1.9.3 Three-dimensional interfaces; 1.10 Eulerian description of material lines and surfaces; 1.10.1 Kinematic compatibility; 1.10.2 Generalized compatibility condition.
- 1.10.3 Line curvilinear coordinates1.10.4 Surface curvilinear coordinates; 1.11 Streamlines, streamtubes, path lines, and streak lines; 1.11.1 Computation of streamlines; 1.11.2 Stream surfaces and streamtubes; 1.11.3 Streamline coordinates; 1.11.4 Path lines and streaklines; 1.12 Vortex lines, vortex tubes, and circulation around loops; 1.12.1 Vortex lines and tubes; 1.12.2 Circulation; 1.12.3 Rate of change of circulation around a material loop; 1.13 Line vortices and vortex sheets; 1.13.1 Line vortex; 1.13.2 Vortex sheet; 1.13.3 Two-dimensional flow; 1.13.4 Axisymmetric flow.
