An optimized hybrid mesh adaptation approach for non-stationary problems applied to air quality modeling

Abstract

In this work, we propose a novel idea that optimizes self-adaptation algorithms for unstructured meshes of domains with complex geometries, applied to nonstationary problems. This idea allows for adapting the spatial mesh at self-detectable instants, according to the values of a parameter calculated as a function of both spatial and temporal indicators. In this algorithm, spatial mesh adaptation using our new approach uses specific strategies of refinement and de-refinement. We validate the efficiency of the proposed algorithm through an air quality forecasting application, employing a numerical model governed by the parabolic PDE of advection-diffusion-reaction type, to forecast sulfur dioxide ($SO_2$) concentrations. The application focuses on a local scale, specifically the Grand Casablanca area (Morocco), using real meteorological data to estimate the PDE parameters.