Numerical Fluid Dynamics

PREFACE: These lecture notes are intended to provide a helpful overview of progress in numerical fluid dynamics, since its conception in the mind of von Neumann 40 years ago. Their main purpose, however, is not to serve as a historical record; still less are they intended present a "state of the art" survey in a rapidly changing field. Instead, their purpose is to supply a thoughtful historical perspective which may help readers to assess future possibilities. Contents: Dynamics of Ideal Fluids; Compressibility and Viscosity; Von Neumann's Influence; Potential Flows; Sound Waves; Nonlinear One-Dimensional Waves; Incompressible Viscous Flows; Lagrangian Dynamical Systems; Conformal Maps and Potential Flows; Fourier Analysis Navier-Stokes Equations; Molecular Models of Matter; 'Courant' Stability Conditions and Amplication Matrices; and Two Dimensional Airfoil Theory.