Assignment 6

First-order transport equation and second-order diffusion equation

Reading assignment and Matlab exercises - Read the following documents:

On first-order transport equation - [Read these documents and try these exercises on your own]

1. Read the chapters 4, 5, and 6, in Vreugdenhil, C.B., 1989
• Documentation and Scripts for Vreughdenhil's Chapter 4 (CompHydExII) - Numerical solutions
• Documentation and Scripts for Vreughdenhil's Chapter 5 - i (CompHydExIII) - Explicit methods
• Documentation and Scripts for Vreughdenhil's Chapter 5 - ii (CompHydExIV) - Leap-frog method
2. Stability, Consistency, and Convergence of Numerical Schemes
• PDF file (compare amplification factor in page 7 with Vreughdenhil's eq. (4.16)
• Maple worksheet - Learn more about Maple here

Characteristics method for Pure Advection - [Read these documents and try these exercises on your own]

1. Characteristics method for pure advection - The Holly-Preissmann approach
2. Online references on Holly-Preissmann and pure advection (optional reading)
• Comparative study of numerical schemes used for one-dimensional transport modelling (pdf file, Gadjos, 1998)
• Numerical Simulation of Unsteady Mobile-bed Hydrodynamics and Contaminant Transport in River Systems (web page)
• Equivalent Differential Equations in Fixed-Grid Characteristics Method (Civil Engineering Data base)
• Interactive Explicit Simulation of 1D Surges and Dam-Break Flow (abstract - International Journal of Numerical Methods in Fluids)
• Unsteady Dispersion of Non-conservative Pollutants in Natural Rivers (Yoo et al.)
• An improved second-moment method for solution of pure-advection problems (Ghods et al.)

Problems to solve

Click here to download a pdf document with the problems to solve Solve only problem [3] in assignment