Trajectory-grid: An accurate sign-preserving advection-diffusion approach for air quality modeling

We propose a new method, called the trajectory-grid (T-G) approach, which contains a fully Lagrangian advection scheme coupled with an Eulerian diffusion scheme, to remove the numerical problems associated with the advection equation in air quality modeling. This method is sign preserving, mass conserving, and very accurate. The method assigns the spatial locations of points on a given concentration profile to a set of concentration pulses; then tracks the pulse positions as they move downwind undergoing diffusion and reactions. Multigrid nesting can be conveniently accounted for by increasing the number density of concentration pulses in given areas in the modeling domain. The method can also serve as a tool to test the validity of the observation-based models. While the execution time may be comparable to that of the Accurate Space Derivative scheme, the advection step of the method is highly amenable to multiply-parallel processing.