An Optimally Stable and Accurate Second‐Order SSP Runge‐Kutta IMEX Scheme for Atmospheric Applications

Abstract

The objective of this paper is to develop an optimized implicit‐explicit (IMEX) Runge‐Kutta scheme for atmospheric applications focusing on stability and accuracy. Following the common terminology, the proposed method is called IMEX‐SSP2(2,3,2), as it has second‐order accuracy and is composed of diagonally implicit two‐stage and explicit three‐stage parts. This scheme enjoys the Strong Stability Preserving (SSP) property for both parts. This new scheme is applied to nonhydrostatic compressible Boussinesq equations in two different arrangements, including (i) semiimplicit and (ii) Horizontally Explicit‐Vertically Implicit (HEVI) forms. The new scheme preserves the SSP property for larger regions of absolute monotonicity compared to the well‐studied scheme in the same class. In addition, numerical tests confirm that the IMEX‐SSP2(2,3,2) improves the maximum stable time step as well as the level of accuracy and computational cost compared to other schemes in the same class. It is demonstrated that the A‐stability property as well as satisfying “second‐stage order” and stiffly accurate conditions lead the proposed scheme to better performance than existing schemes for the applications examined herein.

Mechanisms of Convective Clustering During a 2‐Day Rain Event in AMIE/DYNAMO

“…Held et al (1993) discovered in a 2-D RCE simulation that random convective clouds tend to cluster over time and become aggregated into a single cluster, which was confirmed in later studies (e.g., Bretherton et al, 2005;Tompkins, 2001). More recent studies have suggested the important role of radiation in this self-aggregation (e.g., Muller & Held, 2012;Wing & Emanuel, 2014;Muller & Bony, 2015;Coppin & Bony, 2015;Arnold & Putman, 2018), while others point to moisture-convection feedbacks (Tompkins, 2001;Mapes & Neale, 2011;Colin et al, 2019) and generation of available potential energy (Yang, 2018(Yang, , 2019 as being the dominant mechanism. However, it is not yet clear how convective self-aggregation found in idealized simulations can be related to organized convection in the real world (Wing et al, 2017).…”

Variable tree rooting strategies improve tropical productivity and evapotranspiration in a dynamic global vegetation model

“…their potential physical barriers. Recent data products on global soil depth now enable to better constrain rooting depth in DGVMs (Pelletier et al, 2016).…”

An efficient semi‐implicit temporal scheme for boundary‐layer vertical diffusion

“…Figure illustrates the distribution of the potential temperature θ and the numerical error θ – θ ref which is defined as the difference between the solutions obtained by the nominated approaches and the reference solution calculated by the explicit Runge–Kutta scheme proposed by Rokhzadi et al . () employing very small time‐step resolution, that is, Δ t = 1.0 s. As can be seen in the left‐hand graph, although there are some discrepancies between the LES solutions and the ones obtained by the turbulence modelling, they are still able to produce the general features of the air flow. Referring to the RHS graph, it is clear that all schemes are competitive with minor differences.…”

“…The reference solution was calculated by the explicit Runge–Kutta scheme, proposed by Rokhzadi et al . (), using a very small time‐step resolution, that is, Δ t = 1.0 s. The result was compared to the large‐eddy simulation (LES) solution taken from Beare et al . ().…”