Numerical simulation of atmospheric flow on variable grids using the Galerkin finite element method.

Abstract

A hypothesis is made that the Galerkin Finite Element Method (GFEM) offers a viable option to the traditional Finite Difference Method (FDM) for numerical weather prediction. The shallow water barotropic primitive equations are the forecast equations for all experiments. The hypothesis is tested by observing simple, analytic, atmospheric wave propagation on uniform and variable mesh grids. Second, a strongly forced solution simulating small scale nonlinear interactions is evaluated for both the GFEM and FDM. Finally, a variable, moving grid for a GFEM model is compared to a uniform, higher resolution GFEM model for a strong vortex in a mean flow. The GFEM shows a better propagation for simple atmospheric waves and better prediction to a forced nonlinear solution than the FDM model. A moving variable grid follows an area of strong gradients while not generating noise in the transition zone.