Numerical PDE Techniques for Scientists and Engineers

by: Prof. Dinshaw S. Balsara

Chapter 3: Scalar Advection and Linear Hyperbolic Systems

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

Movies

The following outline of the chapter provides links to 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.

• 3.1) Introduction
• 3.2) Qualitative Introduction to Non-Linear Hybridization for Scalar Advection (Video 1, Video 2, Video 3)
• 3.3) The Total Variation Diminishing Property and Understanding the Limiters (Video 1, Video 2)
• 3.4) Linear Hyperbolic Systems and the Riemann Problem
  • 3.4.1) Solution of Linear Hyperbolic PDEs for Continuous Initial Data
  • 3.4.2) Solution of Linear Hyperbolic PDEs for Discontinuous Initial Data: Simple Waves and the Riemann Problem
  • 3.4.3) The Riemann Problem as a Building Block for the Numerical Solution of Hyperbolic Systems
• 3.5) Numerical Boundary Conditions for Linear Hyperbolic Systems
• 3.6) Second Order Upwind Schemes for Linear Hyperbolic Systems
  • 3.6.1) Second Order Accurate Extension of the Lax-Wendroff Scheme with Limiters
  • 3.6.2) Second Order Accurate, Two-Stage Runge-Kutta Scheme with Limiters
  • 3.6.3) Predictor-Corrector Formulation
  • 3.6.4) Numerical Results from the Previous Three Schemes

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