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

作者：Rokhzadi Arman^*; Mohammadian Abdolmajid; Charron Martin

来源：Journal of Advances in Modeling Earth Systems, 2018, 10(1): 18-42.

DOI：10.1002/2017MS001065

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.