Efficient IMEX Runge-Kutta Methods for Nonhydrostatic Dynamics

Journal Article · Mon Jun 10 04:00:00 EDT 2019 · SIAM Journal on Scientific Computing

OSTI ID:1837626

Steyer, Andrew ^[1]; Vogl, Christopher J. ^[2]; Taylor, Mark ^[1]; Guba, Oksana ^[1]

---

1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

We develop new implicit-explicit Runge-Kutta (IMEX RK) methods for integrating horizontally explicit, vertically implicit (HEVI) partitionings of nonhydrostatic atmosphere models (HEVI models). These new methods, termed IMKG methods, are IMEX RK methods whose explicit part has optimal or near-optimal stability on the imaginary axis and whose implicit part is I-stable. A specialized stability region is presented for characterizing the stability of IMKG and other IMEX methods integrating HEVI models. Subsequently, we formulate two families of IMEX RK methods to enable deriving IMKG methods with a high explicit stage count for integrating HEVI models with large, stable time-steps. Here, we then derive a HEVI partitioning of the HOMME-NH nonhydrostatic model and use this model to compare the accuracy and efficiency of several IMKG methods with other IMEX RK methods from the literature.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC52-07NA27344
• OSTI ID: 1837626
• Report Number(s): LLNL-JRNL--777661; 971533
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing; ISSN 1064-8275
• Publisher: Society for Industrial and Applied Mathematics (SIAM)
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
97 MATHEMATICS AND COMPUTING
HEVI
IMEX method
Runge-Kutta method
atmosphere model
global model
implicit-explicit method
nonhydrostatic
semi-implicit
time-integration