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

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.

• 3.1) Introduction
• 3.2) Qualitative Introduction to Non-Linear Hybridization for Scalar Advection (Slides 1, Slides 2, Slides 3)
• 3.3) The Total Variation Diminishing Property and Understanding the Limiters (Slides 1, Slides 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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