Von neumann stability analysis upwind

1. Is Upwind scheme stable?
2. What is the linear advection equation?

Is Upwind scheme stable?

The upwind scheme is thus called conditionally stable, whereas the downwind and the central scheme are unconditionally unstable.

What is the linear advection equation?

Trivial problem: linear advection equation ⇒ ∂tρ + v∂xρ = 0 ⇒ constant given velocity v ⇒ initial density pulse ρ(x, t = 0) = ρ0(x) • Trivial solution: ρ(x, t) = ρ0(x − vt) ⇒ analytically: done!