Abstract
A monotonic transport algorithm for a high-order time integration scheme is described in this paper. The algorithm is a modified version of an existing high-order time integration scheme, and is tested using a simple one-dimensional pulse and two-dimensional deformational flows. It is found that the new formulation can remove the error, caused by new maxima/minima and excessive smoothing, which occurs in scalar transport using the original extrapolation scheme. The results show that there may be potential for the high-order time integration scheme to be applied in numerical weather prediction models.
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