Abstract
In this chapter we move on to consider the situations where the advection velocity is no longer a constant in time and space. We will introduce techniques to estimate the velocities through the semi-Lagrangian trajectories. We shall consider the arguments for what are referred to as two and three time level schemes. We also consider the case where the advection velocity is a function of the advective quantity itself, where this form of advection is referred to as nonlinear advection. We will introduce the concept of aliasing and nonlinear instability. We finish this chapter by introducing the theory that was developed and applies to limited area models where the departure point could be outside the domain, but also where interior points near the boundary could be dependent on points outside the domain.
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