Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows

Air quality modeling is numerically extremely expensive and, therefore, it requires fast algorithms and sophisticated numerical software. This is due to the fact that reacting flow calculations are highly stiff for time-stepping. In this paper implicit-explicit time integration schemes are derived which use explicit higher order Runge-Kutta schemes for the integration of the horizontal advection. The stiff chemistry and all vertical transport processes (turbulent diffusion, advection, deposition) are integrated in an implicit and coupled manner by a higher order BDF method. High order accuracy and stability conditions are investigated for this class of implicit-explicit schemes. The numerical behavior of the new integration schemes is discussed for a 1D and a simple 3D chemistry-transport problem. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.