A correction method for use in multidimensional time-splitting advection algorithms: Application to two- and three-dimensional transport

Abstract

Meteorological and air quality models rely on accurately solving the advection equation in two and three dimensions. While a number of methods have been developed, all suffer from the formation and growth of errors during the solution procedure. Here, a correction method is developed and applied to the piecewise parabolic method for use in multidimensional modeling. This method is a time-split, alternating direction method with a flux correction to account for diagonal advection. The correction removes over- and undershooting while maintaining the method's accuracy. The analysis also indicates that some methods will have errors that grow significantly in time, while the corrections developed minimize the problem. This analysis found that the buildup of errors was more pronounced in three-dimensional tests, suggesting that this is an import evaluation criteria for other advection algorithms as well.