scholarly journals Multigrid and Runge-Kutta time stepping applied to the uniformly non-oscillatory scheme for conservation laws

1991 ◽  
Vol 25 (3) ◽  
pp. 243-263 ◽  
Author(s):  
J. W. van der Burg ◽  
J. G. M. Kuerten ◽  
P. J. Zandbergen
Keyword(s):  
Conservation Laws ◽  
Time Stepping ◽  
Runge Kutta

scholarly journals High order explicit local time stepping methods for hyperbolic conservation laws

2020 ◽  
Vol 89 (324) ◽  
pp. 1807-1842
Author(s):  
Thi-Thao-Phuong Hoang ◽  
Lili Ju ◽  
Wei Leng ◽  
Zhu Wang
Keyword(s):  
Conservation Laws ◽  
Local Time ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Hyperbolic Conservation ◽  
Time Stepping ◽  
Local Time Stepping

Runge--Kutta-Based Explicit Local Time-Stepping Methods for Wave Propagation

2015 ◽  
Vol 37 (2) ◽  
pp. A747-A775 ◽  
Author(s):  
Marcus J. Grote ◽  
Michaela Mehlin ◽  
Teodora Mitkova
Keyword(s):  
Wave Propagation ◽  
Local Time ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Runge Kutta

scholarly journals A framework to evaluate IMEX schemes for atmospheric models

2020 ◽  
Vol 13 (12) ◽  
pp. 6467-6480
Author(s):  
Oksana Guba ◽  
Mark A. Taylor ◽  
Andrew M. Bradley ◽  
Peter A. Bosler ◽  
Andrew Steyer
Keyword(s):  
Acoustic Waves ◽  
Normal Modes ◽  
Evaluation Framework ◽  
Acoustic System ◽  
Time Stepping ◽  
Imex Schemes ◽  
Runge Kutta ◽  
The Stability ◽  
Implicit And Explicit ◽  
New Framework

Abstract. We present a new evaluation framework for implicit and explicit (IMEX) Runge–Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge–Kutta methods with a high Courant–Friedrichs–Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.

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