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# Introduction to Theoretical and Computational Fluid Dynamics

## byC. Pozrikidis

### Hardcover | April 30, 1999

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Introduction to Theoretical and Computational Fluid Dynamics is the first textbook to combine theoretical and computational aspects of fluid dynamics in a unified and comprehensive treatment. The theoretical developments are carried into the realm of numerical computation, and the numericalprocedures are developed from first principles. This book offers a comprehensive and rigorous introduction to the fundamental principles and equations that govern the kinematics and dynamics of the laminar flow of incompressible Newtonian fluids. It simultaneously illustrates the application of numerical methods to solving a broad range ofproblems drawn from diverse areas, and discusses the development of pertinent computational algorithms. Topics considered include the description and analysis of flow kinematics; the computation of exact solutions of hydrostatics and hydrodynamics by solving ordinary differential equations; thestudy and computation of potential flow; the theory and numerical study of flow at low Reynolds numbers, linear hydrodynamic stability, and vortex motion; boundary-integral methods for potential and Stokes flow; and finite-difference methods for the Navier-Stokes equation. An appendix contains aprimer of numerical methods that allows for ready reference. A unique synthesis of the theoretical and computational aspects of its field, Introduction to Theoretical and Computational Fluid Dynamics serves as an ideal text and source reference for advanced undergraduate students, graduate students, and researchers in the various fields of science andengineering, including mechanical, aeronautical, and chemical engineering, applied mathematics, physics, and computational science. It assumes no prior experience in computational fluid dynamics, and provides references for specialized topics. Each section is followed by theoretical and computerproblems that allow the reader to acquire hands-on experience and simultaneously develop insights into the physics of a variety of flows.

### Details & Specs

Title:Introduction to Theoretical and Computational Fluid DynamicsFormat:HardcoverDimensions:688 pages, 9.49 × 6.73 × 1.46 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0195093208

ISBN - 13:9780195093209

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Table of Contents

Chapter 1: Kinematics of a Flow1.1. Fluid velocity and motion of fluid parcels1.2. Lagrangian labels1.3. Properties of parcels, conservation of mass, and the continuity equation1.4. Material lines, material vectors, and material surfaces1.5. Differential geometry of surfaces1.6. Description of a material surface in Eulerian form1.7. Streamlines, stream tubes, path lines, and streak lines1.8. Vorticity, vortex lines, vortex tubes, and circulation around loops1.9. Line vortices and vortex sheetsChapter 2: Analysis of Kinematics2.1. Irrotational flows and the velocity potential2.2. The reciprocal relation for harmonic functions, and Green's functions of Laplace's equation2.3. Integral representation and further properties of potential flow2.4. The vector potential for incompressible flow2.5. Representation of an incompressible flow in terms in the vorticity2.6. Representation of a flow in terms of the rate of expansion and vorticity2.7. Stream functions for incompressible flow2.8. Flow induced by vorticity2.9. Axisymmetric flow induced by vorticity2.10. Two-dimensional flow induced by vorticityChapter 3: Stresses, the Equation of Motion, and the Vorticity Transport Equation3.1. Forces acting in a fluid, traction, the stress tensor, and the equation of motion3.2. Constitutive relations for the stress tensor3.3. Traction, force, torque, energy dissipation, and the reciprocal theorem for incompressible Newtonian fluids3.4. Navier-Stokes', Euler's and Bernoulli's equation3.5. Equations and boundary conditions governing the motion of an incompressible Newtonian fluid3.6. Traction, vorticity, and flow kinematics on rigid boundaries, free surfaces, and fluid interfaces3.7. Scaling of the Navier-Stokes equation and dynamic similtude3.8. Evolution of circulation around material loops and dynamics of the vorticity field3.9. Computation of exact solutions to the equation of motion in two dimensions based in the vorticity transport equationChapter 4: Hydrostatics4.1. Pressure distribution within a fluid in rigid body motion4.2. The Laplace-Young equation4.3. Two-dimensional interfaces4.4. Axisymmetric interfaces4.5. Three-dimensional interfacesChapter 5: Computing Incompressible Flows5.1. Steady unidirectional flows5.2. Unsteady unidirectional flows5.3. Stagnation-point flows5.4. Flow due to a rotating disk5.5. Flow in a corner due to a point source5.6. Flow due to a point forceChapter 6: Flow at Low Reynolds Numbers6.1. Equations and fundamental properties of Stokes flow6.2. Local solutions in corners6.3. Nearly-unidirectional flows6.4. Flow due to a point force6.5. Fundamental solutions of Stokes flow6.6. Stokes flow past or due to the motion of rigid bodies and liquid drops6.7. Computation of singularity representations6.8. The Lorentz reciprocal theorem and its applications6.9. Boundary integral representation of Stokes flows6.10. Boundary-integral-equation methods6.11. Generalized Faxen's relations6.12. Formulation of two-dimensional Stokes flow in complex variables6.13. Effects of inertia and Oseen flow6.14. Unsteady Stokes flow6.15. Computation of unsteady Stokes flow past or due to the motion of particlesChapter 7: Irrotational Flow7.1. Equations and computation of irrotational flow7.2. Flow past or due to the motion of three-dimensional body7.3. Force and torque exerted on a three-dimensional body7.4. Flow past or due to the motion of a sphere7.5. Flow past or due to the motion of non-spherical bodies7.6. Flow past of due to the motion of two-dimensional bodies7.7. Computation of two-dimensional flow past or due to the motion of a body7.8. Formulation of two-dimensional flow in complex variables7.9. Conformal mapping7.10. Applications of conformal mapping to flow past two-dimesensional bodies7.11. The Schwarz-Christoffel transformation and its applicationsChapter 8: Boundary Layers8.1. Boundary-layer theory8.2. The boundary layer on a semi-infinite flat plate8.3. Boundary layers in acclerating and decelerating flow8.4. Computation of boundary layers around two-dimensional bodies8.5. Boundary layers in axisymmetric and three-dimensional flows8.6. Unsteady boundary layersChapter 9: Hydrodynamic Stability9.1. Evolution equations and forumulation of the linear stability problem9.2. Solution of the initial-value problem and normal-mode analysis9.3. Normal-mode analysisof unidirectional flows9.4. General theorems of the temporal stability of inviscid shear flows9.5. Stability of a uniform layer subject to spatially periodic disturbances9.6. Numerical solution of the Orr-Sommerfeld and Rayleigh equations9.7. Stability of certain classes of unidirectional flows9.8. Stability of a planar interface in potential flow9.9. Viscous interfacial flows9.10. Capillary instability of a curved interface9.11. Inertial instability of rotating fluidsChapter 10: Boundary-Integral Methods for Potential Flow10.1. The boundary-integral equation10.2. Boundary-element methods10.3. Generalized boundary-integral representations10.4. The single-layer potential10.5. The double-layer potential10.6. Investigation of integral equations of the second kind10.7. Regularization of integral equations of the second kind10.8. Completed double-layer representation for exterior flow10.9. Iterative solution of integral equations of the second kindChapter 11: Vortex Motion11.1. Invariants of the motion11.2. Point vortices11.3. Vortex blobs11.4. Two-dimensional vortex sheets11.5. Two-dimensional flows with distributed vorticity11.6. Two-dimensional vortex patches11.7. Axisymmetric flow11.8. Three-dimensional flowChapter 12: Finite-Difference Methods for the Convection-Diffusion Equation12.1. Definitions and procedures12.2. One-dimensional diffusion12.3. Diffusion in two and three dimensions12.4. One-dimensional convection12.5. Convection in two and three dimensions12.6. Convection-diffusion in one dimension12.7. Convection-diffusion in two and three dimensionsChapter 13: Finite-Difference Methods for Incompressible Newtonian Flow13.1. Methods based on the vorticity transport equation13.2. Velocity-pressure formulation13.3. Implementation of methods in primitive variables13.4. Operator splitting, projection, and pressure-correction methods13.5. Methods of modified dynamics or false transientsAppendix A: Index Notation, Differential Operators, and Theorems of Vector CalculusA.1. Index NotationA.2. Vector and matrix products, differential operators in Cartesian coordinatesA.3. Orthogonal curvilinear coordinatesA.4. Differential operators in cylindrical and plane polar coordinatesA.5. Differential operators in spherical polar coordinatesA.6. Integral theorems of vector calculusAppendix B: Primer of Numerical MethodsB.1. Linear algebra equationsB.2. Computation of eigenvaluesB.3. Nonlinear algebraic equationsB.4. Function interpolationB.5. Computation of derivativesB.6. Function integrationB.7. Function approximationB.8. Integration of ordinary differential equationsB.9. Computation of special functions

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