Implicit–explicit Runge–Kutta methods applied to atmospheric chemistry-transport modelling

Abstract

Chemistry-transport calculations are highly stiff in terms of time-stepping. Because explicit ODE solvers require numerous short time steps in order to maintain stability, it seems that especially sparse implicit–explicit solvers are suited to improve the numerical efficiency for atmospheric chemistry applications. In the new version of our mesoscale chemistry-transport model MUSCAT [Knoth, O., Wolke, R., 1998a. An explicit–implicit numerical approach for atmospheric chemistry–transport modelling. Atmospheric Environment 32, 1785–1797.], implicit–explicit (IMEX) time integration schemes are implemented. Explicit second order Runge–Kutta methods for the integration of the horizontal advection are used. The stiff chemistry and all vertical transport processes (turbulent diffusion, advection, deposition) are integrated in an implicit and coupled manner utilizing the second order BDF method. The horizontal fluxes are treated as ‘artificial’ sources within the implicit integration. A change of the solution values as in conventional operator splitting is thus avoided. The aim of this paper is to investigate the interaction between the explicit Runge–Kutta scheme and the implicit integrator. The numerical behavior is discussed for a 1D test problem and 3D chemistry-transport simulations. The efficiency and accuracy of the algorithm are compared to results obtained using the Strang splitting approach. The numerical experiments indicate that our second order implicit–explicit Runge–Kutta methods are a valuable alternative to the conventional operator splitting approach for integrating atmospheric chemistry-transport-models. In mesoscale applications and in cases with stronger accuracy requirements the ‘source splitting’ approach shows a better performance than Strang splitting.