Advection Equation

The advection equation chapter addresses the numerical solution of the one-dimensional linear advection equation, which models the transport of a scalar quantity at constant speed. It examines the stability, accuracy, and phase characteristics of different finite difference schemes, focusing on the influence of the Courant-Friedrichs-Lewy (CFL) condition on stability. The chapter details the impact of discretization on phase and amplitude errors, compares explicit, implicit, Leapfrog, and Crank-Nicolson schemes, and emphasizes the significance of phase and group velocity analysis. By chapter end, readers can assess and implement appropriate schemes for advection problems, understanding their stability and dispersion properties.