Large-Scale Computations with the Unified Danish Eulerian Model

Abstract

The Unified Danish Eulerian Model (UNI-DEM) is an mathematical model for performing different comprehensive studies related to damaging effects from high pollution levels in Denmark and Europe. The model is described with a system of partial differential equations (PDEs). The number of equations is equal to the number of chemical species that are studied by the model. Three chemical schemes (with 35, 56 and 168 chemical species) are available at present. The model can be run either as 1-layer model (a 2-D model) or as 10 layer model (a 3-D model). Three grids can be specified in the horizontal planes: (i) a coarse 96 × 96 grid (corresponding to 50 km × 50 km grid-squares), (ii) a medium 288 × 288 grid (corresponding to 16.67 km × 16.67 km grid-squares), (iii) a fine 480 × 480 grid (corresponding to 10 km × 10 km grid-squares).

The application of some splitting procedure followed by a discretization of the spatial derivatives leads to the solution of several systems of ordinary differential equations (ODEs) at each time-step. The number of equations in each system of ODEs is equal to the product of the number of grid-points and the number of chemical species. If the 480 × 480 horizontal grid is used in the 3-D model with 168 chemical species, then the number of equations in each system of ODEs is equal to N = 480 × 480 × 10 × 168 = 387 072 000. The number of time-steps for a run covering meteorological data for one year is 213 120 (corresponding to a time-stepsize of 150 s). Such huge computational tasks can be treated only if (i) fast numerical methods are selected, (ii) the code is optimized for running on computers with multi-hierarchical memories (i.e. if the caches are properly exploited) and (iii) parallel computers are efficiently used. The success achieved in the efforts to satisfy these three conditions and to carry out long-term computations with UNI-DEM will be reported in this paper. Studies that are related to different important topics have been performed by using the model. The most important of these studies are listed in the end of the paper.