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Extended multirate infinitesimal step methods: Derivation of order conditions
Multirate methods are specially designed for problems with multiple time scales. The multirate infinitesimal step method (MIS) was developed as a generalization of the so called split-explicit Runge–Kutta methods, where the integration of the fast part is conducted analytically. The MIS method was originally evolved for applications related to numerical weather prediction, i.e. the integration of the compressible Euler equation. In this work, an extension to MIS methods will be presented where an arbitrary Runge–Kutta method (RK) is applied for the integration of the fast component. Furthermore, the order convergence from the original MIS method will be reinvestigated including the derivation of conditions up to order four. Additionally will be presented how well-known methods such as recursive flux splitting multirate method, (Schlegel et al., 2012) partitioned Runge–Kutta method, (Jackiewicz and Vermiglio, 2000) and generalized additive Runge–Kutta method, (Sandu and Günther, 2015) are related to or can be cast as an extended MIS method. An exemplary MIS method of order four with five stages will show that the convergence behaviour not only depends on the applied method for the integration of the fast component. The method will further indicate that the used fast time step plays a significant role. © 2019 The Author(s
An Intercomparison of T-REX Mountain-Wave Simulations and Implications for Mesoscale Predictability
Investigations of boundary layer structure, cloud characteristics and vertical mixing of aerosols at Barbados with large eddy simulations
Large eddy simulations (LESs) are performed for the area of the Caribbean island Barbados to investigate island effects on boundary layer modification, cloud generation and vertical mixing of aerosols. Due to the presence of a topographically structured island surface in the domain center, the model setup has to be designed with open lateral boundaries. In order to generate inflow turbulence consistent with the upstream marine boundary layer forcing, we use the cell perturbation method based on finite amplitude potential temperature perturbations. In this work, this method is for the first time tested and validated for moist boundary layer simulations with open lateral boundary conditions. Observational data obtained from the SALTRACE field campaign is used for both model initialization and a comparison with Doppler wind and Raman lidar data. Several numerical sensitivity tests are carried out to demonstrate the problems related to “gray zone modeling” when using coarser spatial grid spacings beyond the inertial subrange of three-dimensional turbulence or when the turbulent marine boundary layer flow is replaced by laminar winds. Especially cloud properties in the downwind area west of Barbados are markedly affected in these kinds of simulations. Results of an additional simulation with a strong trade-wind inversion reveal its effect on cloud layer depth and location. Saharan dust layers that reach Barbados via long-range transport over the North Atlantic are included as passive tracers in the model. Effects of layer thinning, subsidence and turbulent downward transport near the layer bottom at z ≈ 1800 m become apparent. The exact position of these layers and strength of downward mixing is found to be mainly controlled atmospheric stability (especially inversion strength) and wind shear. Comparisons of LES model output with wind lidar data show similarities in the downwind vertical wind structure. Additionally, the model results accurately reproduce the development of the daytime convective boundary layer measured by the Raman lidar
Modelling of atmospheric chemistry-transport processes
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