A Two-Step Adams–Bashforth–Moulton Split-Explicit Integrator for Compressible Atmospheric Models

Split-explicit integration methods used for the compressible Navier–Stokes equations are now used in a wide variety of numerical models ranging from high-resolution local models to convection-permitting climate simulations. Models are now including more sophisticated and complicated physical processes, such as multimoment microphysics parameterizations, electrification, and dry/aqueous chemistry. A wider range of simulation problems combined with the increasing physics complexity may place a tighter constraint on the model’s time step compared to the fluid flow’s Courant number (e.g., the choice of the integration time step based solely on advective Courant number considerations may generate unacceptable errors associated with the parameterization schemes). The third-order multistage Runge–Kutta scheme has been very successful as the split-explicit integration method; however, its efficiency arises partially in its ability to use a time step that is 20%–40% larger than more traditional integration schemes. In applications in which the time step is constrained by other considerations, alternative integration schemes may be more efficient. Here a two-step third-order Adams–Bashforth–Moulton integrator is stably split in a similar manner as the split Runge–Kutta scheme. For applications in which the large time step is not constrained by the advective Courant number it requires less computational effort. Stability is demonstrated through eigenvalue analysis of the linear coupled one-dimensional velocity–pressure equations, and full two-dimensional nonlinear solutions from a standard test problem are shown to demonstrate solution accuracy and efficiency.