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Preface | p. ix |
Flow Topics Governed by Ordinary Differential Equations: Initial-Value Problems | p. 1 |
Numerical Solution of Ordinary Differential Equations: Initial-Value Problems | p. 1 |
Free Falling of a Spherical Body | p. 5 |
Computer Simulation of Some Restrained Motions | p. 13 |
Fourth-Order Runge-Kutta Method for Computing Two-Dimensional Motions of a Body through a Fluid | p. 22 |
Ballistics of a Spherical Projectile | p. 24 |
Flight Path of a Glider-A Graphical Presentation | p. 32 |
Rolling Up of the Trailing Vortex Sheet behind a Finite Wing | p. 35 |
Appendix | p. 44 |
Inviscid Fluid Flows | p. 50 |
Incompressible Potential Flows | p. 51 |
Numerical Solution of Second-Order Ordinary Differential Equations: Boundary-Value Problems | p. 55 |
Radial Flow Caused by Distributed Sources and Sinks | p. 60 |
Inverse Method I: Superposition of Elementary Flows | p. 61 |
von Kármán's Method for Approximating Flow Past Bodies of Revolution | p. 69 |
Inverse Method II: Conformal Mapping | p. 76 |
Classification of Second-Order Partial Differential Equations | p. 87 |
Numerical Methods for Solving Elliptic Partial Differential Equations | p. 90 |
Potential Flows in Ducts or around Bodies-Irregular and Derivative Boundary Conditions | p. 96 |
Numerical Solution of Hyperbolic Partial Differential Equations | p. 105 |
Propagate-and Reflection of a Small-Amplitude Wave | p. 110 |
Propagation and Reflection of a Small-Amplitude Wave | p. 110 |
Propagation of a Finite-Amplitude Wave: Formation of a Shock | p. 120 |
An Application to Biological Fluid Dynamics: Flow in an Elastic Tube | p. 128 |
Appendix | p. 143 |
Viscous Fluid Flows | p. 145 |
Governing Equations for Viscous Flows | p. 145 |
Self-Similar Laminar Boundary-Layer Flows | p. 147 |
Hit-Plate Thermometer Problem-Ordinary Boundary-Value Problems Involving Derivative Boundary Conditions | p. 157 |
Pipe and Oren-Channel Flows | p. 163 |
Explicit Methods for Solving Parabolic Partial Differential Equations-Generalized Rayleigh Problem | p. 168 |
Implicit Methods for Solving Parabolic Partial Differential Equations-Starting Flow in a Channel | p. 173 |
Numerical Solution of Biharmonic Equations-Stokes Flows | p. 179 |
Flow Stability and Pseudo-Spectral Methods | p. 185 |
Appendix | p. 207 |
Numerical Solution of the Incompressible Navier-Stokes Equation | p. 215 |
Flow around a Sphere at Finite Reynolds Numbers-Galerkin Method | p. 216 |
Upwind Differencing and Artificial Viscosity | p. 229 |
Benard and Taylor Instabilities | p. 234 |
Primitive Variable Formulation: Algorithmic Considerations | p. 249 |
Primitive Variable Formulation: Numerical Integration of the Navier-Stokes Equation | p. 258 |
Flow Past a Circular Cylinder: An Example for the Vorticity-Stream Function Formulation | p. 280 |
Appendix | p. 297 |
Bibliography | p. 298 |
Index | p. 303 |
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