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

Abstract

Twenty years ago, the multidimensional, positive deÿnite, 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-to meso-) 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 e ciency using analytic and idealized test cases.

Advection of Microphysical Scalars in Terminal Area Simulation System (TASS)

“…The computed results from different schemes are also compared with the exact solution along the mesh centerline in Figure 11 for different mesh resolutions. The computed results for all schemes are in excellent agreement with the exact solution (see, e.g., Hólm 1995, Ahmad et al 2006). The behaviors of the MUSCL-type scheme and the highresolution wave propagation method are quite similar.…”

Three-Dimensional Finite Element Modelling of Stack Pollutant Emissions

“…As α 1 and α 2 are constant in Ω, the variational approach results in an elliptic problem in φ, by substituting (4) in (1), that is solved by using the finite element method.…”

“…Three remarkable uses of unstructured meshes in atmospheric pollution problems are the two-dimensional regional-global examples presented in [19,1], the threedimensional regional examples, including local refinement with element sizes of 2km, presented in [39], and the three-dimensional tetrahedral meshes for local wind field analysis with element sizes ranging from two meters up to two kilometres, see [25,27]. The ideas of this last approach are considered to include the plume rise effect in the wind field that is used in the air quality problem.…”

“…Several twodimensional [41] and three-dimensional [26,28,10] adaptive finite element solutions have been developed by the authors. The convection, diffusion and reaction problem is usually solved using splitting schemes [22,6] and specific numerical solvers for time integration of photochemical reaction terms [36,35,1]. In this paper a stabilized finite element formulation with a Crank-Nicolson temporal integration is proposed to solve the problem [7,33].…”

Finite Element Simulation of Chimney Emissions: A Proposal for Near Field Impact Assessment in Highly Complex Terrains

“…Three remarkable applications of non-structured meshes to atmospheric pollution problems can be found: 2D global-regional examples [17,18], 3D regional examples with element refinement down to two kilometers [19], and 3D local wind simulations with element sizes ranging from two meters up to two kilometers [20,21,22]. Last approach is the one used in this work, although here it is also applied to simulate transport -reaction problems.…”