A two-dimensional finite element advection model with variable resolution.

Abstract

Many meteorological forecast applications require the use of grids that have a high resolution in a particular area of interest, while allowing coarser resolution elsewhere. Conventional finite difference models often use nested grids to this end. In recent years, finite element models have been offered as an alternative. In this study, the two-dimensional advection equation with diffusion is defined over a rectangular domain. The Galerkin technique is applied to linear basis functions on triangular elements. The model is tested to determine the sensitivity of the forecast to various nodal geometries. Both equilateral and right triangular elements are tested. It is found that the equilateral arrangement consistently yields a superior forecast. Other tests are conducted in which the resolution is varied smoothly versus abruptly over the domain. The smoothly varying case gives results that are dramatically improved over the abruptly varying case. Among the conclusions is the fact that, for a given maximum resolution, the more slowly and smoothly the element size is changed, the better the forecast obtained.