Fluid Dynamics Theory, Computation, and Numerical Simulation

• Main Author: Pozrikidis, C
• Format: eBook Book
• Language: English
• Published: New York, NY Springer Nature 2016; Springer; Springer US
• Edition: 3
• Subjects: Engineering; Engineering & allied operations; Engineering Fluid Dynamics; Fluid dynamics; Fluid- and Aerodynamics; Mathematical and Computational Engineering; Programming Techniques; Theoretical, Mathematical and Computational Physics
• ISBN: 1489979913; 9781489979919; 9781489979902; 1489979905
• DOI: 10.1007/978-1-4899-7991-9

This is the first book that extends the classical field of fluid dynamics into the realm of scientific computing. It is both comprehensive and accessible to the beginner. The book is supplemented by a free web-based software library, FDLIB, and MatLab.

Table of Contents:

• 2.10.1 The no-penetration boundary condition -- Impermeable solid boundaries -- Rigid-body motion -- The no-penetration condition in terms of the stream function -- Sharp interfaces -- Problems -- 2.10.1 Changing the center of rotation -- 2.10.2 Stream functions -- Chapter 3 Flow computation based on kinematics -- 3.1 Flow classification based on kinematics -- Irrotational flows -- Vortex flows -- Rotational flows -- Flows in nature and technology -- Flow computation -- Problem -- 3.1.1 Flow classification -- 3.2 Irrotational flow and the velocity potential -- 3.2.1 Two-dimensional flow -- The velocity potential -- Deriving the potential -- Computation of the potential based on kinematics -- 3.2.2 Incompressible fluids and the harmonic potential -- Quasi-steady state -- 3.2.3 Three-dimensional flow -- 3.2.4 Boundary conditions -- Impermeable boundaries -- Permeable boundaries -- 3.2.5 Cylindrical polar coordinates -- 3.2.6 Spherical polar coordinates -- 3.2.7 Plane polar coordinates -- Problems -- 3.2.1 Deriving the velocity potential -- 3.2.2 Irrotational flow in cylindrical polar coordinates -- 3.2.3 Irrotational flow in spherical polar coordinates -- 3.2.4 Irrotational flow in plane polar coordinates -- 3.3 Finite-difference methods -- 3.3.1 Boundary conditions -- 3.3.2 Finite-difference grid -- Dirichlet boundary condition -- 3.3.3 Finite-difference discretization -- Neumann boundary condition -- Algebraic balance -- 3.3.4 Compilation of a linear system -- Southwestern corner node -- Southwestern bordering node -- Other nodes -- Assembly -- Solving the linear system -- Problems -- 3.3.1 Explicit form of a linear system -- 3.3.2 Neumann boundary conditions all around -- 3.3.3 Irrotational flow in a cavity -- 3.4 Linear solvers -- 3.4.1 Gauss elimination -- Pivoting -- 3.4.2 A menagerie of other methods -- Iterative methods -- Problem
• 3.4.1 Gauss elimination
• Spherical polar coordinates -- Plane polar coordinates -- Problems -- 2.1.1 Inner vector product -- 2.1.2 Decomposition of a linearized flow -- 2.2 Fluid parcel expansion -- Divergence of the velocity field -- Solenoidal velocity fields -- Problem -- 2.2.1 Rate of expansion -- 2.3 Fluid parcel rotation and vorticity -- Outer vector product -- Interpretation of the outer vector product -- 2.3.1 Curl and vorticity -- Irrotational flow -- The alternating tensor -- 2.3.2 Two-dimensional flow -- 2.3.3 Axisymmetric flow -- Problems -- 2.3.1 Properties of the outer vector product -- 2.3.2 Properties of Kronecker's delta and alternating tensor -- 2.3.3 Relation between the vorticity tensor and vector -- 2.3.4 The vorticity field is solenoidal -- 2.4 Fluid parcel deformation -- Computation of the rates of strain -- Problems -- 2.4.1 Properties of eigenvalues -- 2.4.2 Eigenvalues and eigenvectors -- 2.5 Numerical differentiation -- 2.5.1 Numerical differentiation in one dimension -- First-order differentiation -- Second-order differentiation -- 2.5.2 Numerical differentiation in two dimensions -- First-order differentiation -- Second-order differentiation -- 2.5.3 Velocity gradient and related functions -- Problems -- 2.5.1 Numerical differentiation -- 2.5.2 Numerical differentiation of a two-dimensional flow -- 2.6 Flow rates -- Unit tangent and unit normal vectors -- Normal and tangential velocities -- 2.6.1 Areal flow rate and flux -- 2.6.2 Areal flow rate across a line -- Parcel expansion -- 2.6.3 Analytical integration -- 2.6.4 Numerical integration -- Trapezoidal rule -- 2.6.5 The Gauss divergence theorem in two dimensions -- Areal flow rate across a loop -- Incompressible fluids -- 2.6.6 Flow rate in a three-dimensional flow -- 2.6.7 Gauss divergence theorem in three dimensions -- Flow rate -- 2.6.8 Axisymmetric flow -- Problems
• Intro -- Contents -- Preface -- FDLIB -- Third edition -- Notation -- Chapter 1 Introduction to kinematics -- 1.1 Fluids and solids -- Intermolecular forces -- Problems -- 1.1.1 Nature of a liquid/solid suspension -- 1.1.2 Water and milk -- 1.2 Fluid parcels and flow kinematics -- Decomposition of a fluid into parcels -- Relative parcel motion -- Kinematics as a field of fluid dynamics -- Problem -- 1.2.1 Athens, Ohio -- 1.2.2 A rolling sphere -- 1.3 Coordinates, velocity, and acceleration -- Unit vectors -- Velocity -- Acceleration -- 1.3.1 Cylindrical polar coordinates -- Unit vectors -- Position and velocity -- Relation to Cartesian vector components -- Rates of change -- Velocity components -- Acceleration -- 1.3.2 Spherical polar coordinates -- Unit vectors -- Position and velocity -- Relation to Cartesian vector components -- Rates of change -- Velocity components -- Acceleration -- 1.3.3 Plane polar coordinates -- Unit vectors -- Position and velocity -- Relation to Cartesian vector components -- Rates of change -- Velocity components -- Acceleration -- Problems -- 1.3.1 Spherical polar coordinates -- 1.3.2 Acceleration -- 1.4 Fluid velocity -- 1.4.1 Continuum approximation -- 1.4.2 Steady flow -- 1.4.3 Two-dimensional flow -- 1.4.4 Swirling and axisymmetric flow -- 1.4.5 Velocity vector field, streamlines and stagnation points -- Problems -- 1.4.1 Units of coefficients -- 1.4.2 Streamline patterns -- 1.5 Point particles and their trajectories -- 1.5.1 Path lines -- Instantaneous streamlines -- 1.5.2 Ordinary differential equations (ODEs) -- Unidirectional flow -- Method of integrating factors -- Steady linear flow -- Eigenvalues and eigenvectors -- Steady linear flows with drift -- 1.5.3 Explicit Euler method -- Algorithm -- 1.5.4 Modified Euler method -- Program path lines -- 1.5.5 Description in polar coordinates -- 1.5.6 Streaklines
• Problems -- 1.5.1 Streamlines by analytical integration -- 1.5.2 Streamlines by analytical integration -- 1.5.3 Path lines by numerical integration -- 1.5.4 Streamlines by numerical integration -- 1.6 Material surfaces and elementary motions -- Material parcels -- 1.6.1 Fluid parcel rotation -- 1.6.2 Fluid parcel deformation -- 1.6.3 Fluid parcel expansion -- 1.6.4 Superposition of rotation, deformation, and expansion -- 1.6.5 Rotated coordinates -- Rotation matrix -- Velocities -- 1.6.6 Fundamental decomposition of a two-dimensional flow -- Eigenvalues and eigenvectors -- A typical linear flow -- Simple shear flow -- Problems -- 1.6.1 Material lines -- 1.6.2 Rotation of coordinates -- 1.6.3 Fundamental decomposition of a flow -- 1.7 Numerical interpolation -- 1.7.1 Interpolation in one dimension -- Linear interpolation -- Quadratic interpolation -- 1.7.2 Interpolation in two dimensions -- Cartesian grid -- Grid generation -- Bilinear interpolation -- 1.7.3 Interpolation of the velocity in a two-dimensional flow -- 1.7.4 Streamlines by interpolation -- Problems -- 1.7.1 Quadratic interpolation -- 1.7.2 Forward-point parabolic interpolation -- 1.7.3 Trilinear interpolation -- 1.7.4 Bilinear interpolation -- 1.7.5 Streamlines by interpolation -- Chapter 2 More on kinematics -- 2.1 Fundamental modes of fluid parcel motion -- 2.1.1 Function linearization -- Taylor series -- Gradient of a scalar function -- Inner vector product -- Interpretation of the inner vector product -- Linearized expansion in compact form -- 2.1.2 Velocity gradient tensor -- An application -- What is a tensor? -- 2.1.3 Relative motion of point particles -- 2.1.4 Fundamental motions in two-dimensional flow -- Areal expansion -- Rotation -- Deformation -- 2.1.5 Fundamental motions in three-dimensional flow -- 2.1.6 Gradient in polar coordinates -- Cylindrical polar coordinates
• 2.6.1 Flow rate across an ellipse -- 2.6.2 Flow rate across an ellipse -- 2.7 Mass conservation and the continuity equation -- 2.7.1 Mass flux and mass flow rate -- 2.7.2 Mass flow rate across a closed line -- 2.7.3 The continuity equation -- Differential mass balance -- 2.7.4 Three-dimensional flow -- 2.7.5 Control volume and integral mass balance -- 2.7.6 Rigid-body translation -- 2.7.7 Evolution equation for the density -- Temporal discretization -- Finite-difference method -- Algorithm -- 2.7.8 Continuity equation for axisymmetric flow -- Problems -- 2.7.1 Convection under constant velocity -- 2.7.2 Steady state -- 2.7.3 Finite-difference method -- 2.8 Properties of point particles -- 2.8.1 The material derivative -- Taylor series expansion -- Moving with the fluid -- Lagrangian and Eulerian derivatives -- 2.8.2 The continuity equation -- 2.8.3 Point particle acceleration -- Linear momentum -- Cylindrical polar coordinates -- Spherical polar coordinates -- Plane polar coordinates -- Acceleration at a point with zero vorticity -- Problems -- 2.8.1 Properties of the material derivative -- 2.8.2 Point particle acceleration in rotational flow -- 2.8.3 Point particle motion in one-dimensional flow -- 2.9 Incompressible fluids and stream functions -- 2.9.1 Kinematic consequence of incompressibility -- 2.9.2 Mathematical consequence of incompressibility -- 2.9.3 Stream function for two-dimensional flow -- Extensional flow -- Non-uniqueness of the stream function -- Physical interpretation -- Vorticity -- Plane polar coordinates -- 2.9.4 Stream function for axisymmetric flow -- Extensional flow -- Physical interpretation -- Vorticity -- Spherical polar coordinates -- Problems -- 2.9.1 Stream function for two-dimensional flow -- 2.9.2 Stream function of axisymmetric flow -- 2.10 Kinematic conditions at boundaries -- Types of boundary conditions