Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models

The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods...

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Bibliographic Details
Published in:Geoscientific Model Development 2018-04, Vol.11 (4), p.1497-1515
Main Authors: Gardner, David J, Guerra, Jorge E, Hamon, François P, Reynolds, Daniel R, Ullrich, Paul A, Woodward, Carol S
Format: Article
Language:English
Subjects:
Accuracy
Acoustic waves
Additives
Atmospheric circulation
Atmospheric dynamics
Atmospheric models
Baroclinic waves
Communication
Computer simulation
Dynamic stability
Dynamics
Efficiency
ENVIRONMENTAL SCIENCES
Formulations
GEOSCIENCES
Gravitational waves
Gravity
Gravity waves
Mathematical models
MATHEMATICS AND COMPUTING
Methods
Nonlinear systems
Numerical analysis
Ordinary differential equations
Run time (computers)
Runge-Kutta method
Simulation
Sound waves
Time integration
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Summary:The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored.The accuracy and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.
ISSN:1991-9603
1991-959X
1991-962X
1991-9603
1991-962X
DOI:10.5194/gmd-11-1497-2018