Numerical PDE Techniques for Scientists and Engineers

by: Prof. Dinshaw S. Balsara

Chapter 4: Non-Linear Conservation Laws; the Scalar Case

• Abstract
• Movies
• Slides with Voice-Over
• Chapters, Codes, Etc
• Textbook Home

Movies

The following video lectures are available for this chapter. Please use Chrome or Firefox to download the movies to your disk. Then play the movies with VLC.

• 4.1) Introduction
• 4.2) A Gentle Introduction to Rarefaction Waves and Shocks
  • 4.2.1) A Mechanistic Model for Rarefaction Waves and Shocks
  • 4.2.2) The Formation of Shocks and Rarefaction Waves
  • 4.2.3) Shock and Rarefaction Wave Solutions Arising from the Burgers Equation
  • 4.2.4) Simple Wave Solutions of the Burgers Equation
• 4.3) Isolated Shock Waves
  • 4.3.1) Shocks as Solutions of Viscous Equations that are Taken to the Inviscid Limit
  • 4.3.2) Shocks as Weak Solutions of a Hyperbolic Equation
• 4.4) Isolated Rarefaction Fans
  • 4.4.1) The Structure of an Isolated Rarefaction Fan
  • 4.4.2) The Role of Entropy in Arbitrating the Evolution of Discontinuities
• 4.5) The Entropy Fix and Approximate Riemann Solvers
  • 4.5.1) The Entropy Fix
  • 4.5.2) Approximate Riemann Solvers — The HLL and LLF Riemann Solvers
• 4.6) Boundary Conditions
• 4.7) Numerical Methods

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