Efficient IMEX Runge-Kutta methods for nonhydrostatic dynamics

Abstract

We analyze the stability and accuracy (up to third order) of a new family of implicit-explicit Runge-Kutta (IMEX RK) methods. This analysis expedites development of methods with various balances in the number of explicit stages and implicit solves. We emphasize deriving methods with large stability regions for horizontally explicit vertically implicit (HEVI) partitionings of nonhydrostatic atmosphere models. The IMKG2 and IMKG3 families of IMEX RK methods are formulated within this framework. The HOMME-NH model with a HEVI partitioning is used for testing the accuracy and stability of various IMKG2-3 methods. The efficiency of several IMKG2-3 methods is demonstrated in HOMME-NH and compared to other IMEX RK methods in the literature.