Application of the multidimensional positive definite advection transport algorithm (MPDATA) to environmental modelling on adaptive unstructured grids

Twenty years ago, the multidimensional, positive definite, advection transport algorithm was introduced by Smolarkiewicz. Over the two decades since, it has been applied countless times to numerous problems, however almost always on rectilinear grids. One of the few exceptions is the Operational Multiscale Environment model with Grid Adaptivity (OMEGA), an atmospheric simulation system originally designed to simulate atmospheric dispersion in the planetary boundary layer, but since then used for both mesoscale (from meso‐α to meso‐γ) dispersion and weather forecasting. One of the unique aspects of OMEGA is the triangular unstructured grid geometry which leads in a natural way to the creation of a global grid with continuously variable resolution from roughly 100 km over the oceans to less than 10 km over regions of interest. Another unique aspect is the concept of dynamically adapting grid resolution—sometimes also called solution‐adaptive grid resolution. A central element of the modelling system, however, is its advection solver—MPDATA. This paper presents the implementation of MPDATA on an unstructured grid and demonstrates its accuracy and efficiency using analytic and idealized test cases. Copyright © 2005 John Wiley & Sons, Ltd.