Numerical PDE Techniques for Scientists and Engineers

by: Prof. Dinshaw S. Balsara

Chapter 1: An Overview of PDEs

• Abstract
• Movies
• Slides with Voice-Over
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Slides with Voice-Over

The following slides with Voice-Over (i.e. light-weight mp4 movies) are available for this chapter. Please use Chrome or Firefox to download the movies to your disk. Then play the movies with VLC.

• 1.1) Introduction
• 1.2) Derivation of the Fluid Equations
  • 1.2.1) The Role of Collisions
  • 1.2.2) The Boltzmann Equation
  • 1.2.3) Moments of the Boltzmann Equation
  • 1.2.4) The Continuity Equation
  • 1.2.5) The Momentum Equation
  • 1.2.6) The Energy Equation
• 1.3) The Euler Equations
• 1.4) The Navier-Stokes Equations
• 1.5) Classifying and Understanding PDEs
  • 1.5.1) Motivation
  • 1.5.2) Characteristic Analysis of the Euler Equations
  • 1.5.3) Generalized Definition of a Hyperbolic PDE
  • 1.5.4) Analysis of the Navier Stokes Equations
• 1.6) Incompressible Flow Equations
• 1.7) The Shallow Water Equations
• 1.8) Maxwell’s Equations
• 1.9) The Magnetohydrodynamic Equations
• 1.10) Flux Limited Diffusion Radiation Hydrodynamics
• 1.11) The Radiative Transfer Equation
• 1.12) The Equations of Linear Elasticity
• 1.13) Relativistic Hydrodynamics and Magnetohydrodynamics

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