Dale Durran

Department of Atmospheric Sciences, University of Washington

Lecture 1: Where is GFD's Room in the House of Partial Differential Equations?

We will consider the relation between waves and characteristics and the reason that geophysical flows tend to be relatively free from shocks (though not poorly resolved gradients). Despite the smooth nature of our solutions, we demonstrate that some form of numerical dissipation is nevertheless required to prevent nonlinear instability.

Lecture 2: Dissipation and Dispersion in Numerical Solutions to Linear Wave Equations

Sources of dissipation and dispersion are identified in solutions to the linear one-way wave equation. Global strategies for minimizing these errors are discussed and contrasted with strategies local strategies for reducing errors near steep gradients via flux limiter and ENO methods.

Lecture 3: Two Significant Numerical Challenges in Atmospheric Modeling}

The first challenge is to design efficient methods for the treatment of slowly evolving flows when the underlying dynamics also support very fast moving waves. The second is to design appropriate boundary conditions for limited area models.