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Combination of WENO and Explicit Runge–Kutta Methods for Wind Transport in the Meso-NH Model

Lunet, Thibaut and Lac, Christine and Auguste, Franck and Visentin, Florian and Masson, Valéry and Escobar, Juan Combination of WENO and Explicit Runge–Kutta Methods for Wind Transport in the Meso-NH Model. (2017) Monthly Weather Review, 145 (9). 3817-3838. ISSN 0027-0644

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Official URL: http://dx.doi.org/10.1175/MWR-D-16-0343.1

Abstract

This paper investigates the use of the weighted essentially nonoscillatory (WENO) space discretization methods of third and fifth order for momentum transport in the Meso-NH meteorological model, and their association with explicit Runge–Kutta (ERK) methods, with the specific purpose of finding an optimal combination in terms of wall-clock time to solution. A linear stability analysis using von Neumann theory is first conducted that considers six different ERK time integration methods. A new graphical representation of linear stability is proposed, which allows a first discrimination between the ERK methods. The theoretical analysis is then completed by tests on numerical problems of increasing complexity (linear advection of high wind gradient, orographic waves, density current, large eddy simulation of fog, and windstorm simulation), using a fourth-order-centered scheme as a reference basis. The five-stage third-order and fourth-order ERK combinations appear as the time integration methods of choice for coupling with WENO schemes in terms of stability. An explicit time-splitting method added to the ERK temporal scheme for WENO improves the stability properties slightly more. When the spatial discretizations are compared, WENO schemes present the main advantage of maintaining stable, nonoscillatory transitions with sharp discontinuities, but WENO third order is excessively damping, while WENO fifth order provides better accuracy. Finally, WENO fifth order combined with the ERK method makes the whole physics of the model 3 times faster compared to the classical fourth-order centered scheme associated with the leapfrog temporal scheme.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Airbus (FRANCE)
French research institutions > Centre National d'Études Spatiales - CNES (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > EDF (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
Other partners > Total (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > Institut national des sciences de l'Univers - INSU (FRANCE)
Other partners > Météo France (FRANCE)
Other partners > SAFRAN (FRANCE)
Laboratory name:
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Deposited By: Thibaut Lunet
Deposited On:19 Feb 2018 09:28

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