Abstract
Chapter 3 is an introduction to numerical modeling of advective transport using finite-difference methods. The concept of upwinding is introduced, and the behavior of several methods is compared and contrasted. A more detailed examination of spurious waves is presented, and models are constructed for the simultaneous transport by advection and diffusion. The Courant-Friedrichs-Lewy condition is explained. The Lax-Friedrichs and Lax-Wendroff methods are introduced, and their algorithmic properties are presented. Parasitic waves, numerical dissipation, and dispersion are analyzed, and their impact on the numerical solution is explained. Models for advection coupled with diffusion are developed, and a generalized upwind method is introduced.
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