Combination of WENO and Explicit Runge-Kutta methods for wind transport in Meso-NH model
Lunet, Thibaut ; Lac, Christine ; Auguste, Franck ; Visentin, Florian ; Masson, Valéry ; Escobar, Juan
This paper investigates the use of the Weighted Essentially Non Oscillatory (WENO) space discretization methods of 5th and 3rd order for momentum transport in the meteorological model Meso-NH, 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 considering 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 wind-storm simulation), using a 4-th order centered scheme as a reference basis. The 5-stages 3-order and the 4-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, non-oscillatory transitions with sharp discontinuities, but WENO 3rd order is excessively damping, while WENO 5th order presents better accuracy. Finally, WENO 5th order combined with the ERK method makes the whole physics of the model 3 times faster compared to the classical 4-th order centered scheme associated with the leapfrog temporal scheme.
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