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.
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