The Analytical Solution to the One-Dimensional Advection equation can be written as q(x,t) = sin(k(x-Ut)) where k is the wavenumber.
Wavelength:Lx = 3000km
U = 10m/s
Advection equation : dq/dt = del(q)/del(t) + U*del(q)/del(x)
We suppose the wave is represented on a 32Δx grid
Courant-Friedrichs-Lewy (CFL) C=1
1- Write a Matlab script that draws the function q(x,t) at t = 0.
2- Solve numerically the advection equation using the central difference method. Choose appropriate boundary conditions so that the wave is entering on the left side (west side) and is coming out on the right side (east side). Show on the same graph both the analytical solution and numerical solution at the first timestep (N=1).