Notes on Advection

where a(x, t) is some scalar quantity and u is the velocity at which it is advected (u > 0 advects to the right). The solution to Eq. 1 is to simply take the initial data, a(x, t = 0), and displace it to the right at a speed u. The shape of the initial data is preserved in the advection. Many hyperbolic systems of PDEs, e.g. the equations of hydrodynamics, can be written in a form that looks like a system of (nonlinear) advection equations, so the advection equation provides important insight into the methods used for these systems.