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5 - Numerical Methods for Advection–Diffusion Equations

Published online by Cambridge University Press:  02 February 2023

Tian-Chyi Jim Yeh ,
Yanhui Dong  and
Shujun Ye
Tian-Chyi Jim Yeh
Affiliation:
University of Arizona
Yanhui Dong
Affiliation:
Chinese Academy of Sciences, Beijing
Shujun Ye
Affiliation:
Nanjing University, China
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Summary

This chapter introduces numerical methods, including 1) Finite Difference Approach, 2) Methods of characteristics (Eulerian-Lagrangian), and 3) Finite Element Approach for solving the ADE applicable to multidimensional, variable velocity, irregular boundary, and initial conditions. However, only one- and two-dimension examples are illustrated for convenience. Once the algorithms are understood, they can be expanded to other situations with ease.

Keywords

finite differencenuerical dispersionmesh Peclet numberCourant Numbermethod of characteristicsfinite elementshape functionglobal matrix
Type
Chapter
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An Introduction to Solute Transport in Heterogeneous Geologic Media , pp. 123 - 156
Publisher: Cambridge University Press
Print publication year: 2023

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