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1 Flow Topics Governed by Ordinary Differential Equations: Initial-Value Problems.
1.1 Numerical Solution of Ordinary Differential Equations: Initial-Value Problems.
1.2 Free Falling of a Spherical Body.
1.3 Computer Simulation of Some Restrained Motions.
1.4 Fourth-Order Runge-Kutta Method for Computing Two-Dimensional Motions of a Body Through a Fluid.
1.5 Ballistics of a Spherical Projectile.
1.6 Flight Path of a Glider – A Graphical Presentation.
1.7 Rolling Up of the Trailing Vortex Sheet Behind a Finite Wing.
2 Inviscid Fluid Flows.
2.1 Incompressible Potential Flows.
2.2 Numerical Solution of Second-Order Ordinary Differential Equations: Boundary-Value Problems.
2.3 Radial Flow Caused by Distributed Sources and Sinks.
2.4 Inverse Method I: Superposition of Elementary Flows.
2.5 von Kármán’s Method for Approximating Flow Past Bodies of Revolution.
2.6 Inverse Method II: Conformal Mapping.
2.7 Classification of Second-Order Partial Differential Equations.
2.8 Numerical Methods for Solving Elliptic Partial Differential Equations.
2.9 Potential Flows in Ducts or Around Bodies – Irregular and Derivative Boundary Conditions.
2.10 Numerical Solution of Hyperbolic Partial Differential Equations.
2.11 Propagation and Reflection of a Small-Amplitude Wave.
2.12 Propagation of a Finite-Amplitude Wave: Formation of a Shock.
2.13 An Application to Biological Fluid Dynamics: Flow in an Elastic Tube.
3 Viscous Fluid Flows.
3.1 Governing Equations for Viscous Flows.
3.2 Self-Similar Laminar Boundary-Layer Flows.
3.3 Flat-Plate Thermometer Problem – Ordinary Boundary-Value Problems Involving Derivative Boundary Conditions.
3.4 Pipe and Open-Channel Flows.
3.5 Explicit Methods for Solving Parabolic Partial Differential Equations-Generalized Rayleigh Problem.
3.6 Implicit Methods for Solving Parabolic Partial Differential Equations-Starting Flow in a Channel.
3.7 Numerical Solution of Biharmonic Equations – Stokes’ Flows.
3.8 Flow Stability and Pseudo-Spectral Methods.
4 Numerical Solution of the Incompressible Navier Stokes Equations.
4.1 Flow Around a Sphere at Finite Reynolds Numbers – Galerkin Method.
4.2 Upwind Differencing and Artificial Viscosity.
4.3 Bénard and Taylor Instabilities.
4.4 Primitive Variable Formulation: Algorithmic Considerations.
4.5 Primitive Variable Formulation: Numerical Integration of the Navier-Stokes Equation.
4.6 Flow Past a Circular Cylinder: An Example For the Vorticity-Stream Function Formulation.