Alternatives to the Robert–Asselin filter

Patrick Marsaleix (1) , Francis Auclair (1) , Thomas Duhaut (1) , Claude Estournel (1) , Cyril Nguyen (2) , Caroline Ulses (1)

1 LAERO - Laboratoire d'aérologie
2 ECOLA - Echanges Côte-Large

The Leap Frog time stepping scheme (hereafter LF) partly loses its conservation properties when a Robert-Asselin filter (hereafter RA) is used to damp the computational mode. The LF + RA scheme actually leads to a well-known long term attenuation of the physical mode. Besides, the stability of the LF, e.g. the maximum permitted time step, is lowered by the use of the RA. Several methods, derived from the Laplacian approach of Marsaleix et al. (2008), are presented as an alternative to the RA. It appears that the physical mode is eventually much less impacted by higher order time filters. However, in some cases, the stability of the time stepping scheme becomes worse than that of the LF + RA. A five points scheme finally appears to preserve both the amplitude of the physical mode and the stability of the time stepping scheme. The analysis of these filters is based on a triple approach: the kinetic energy balance, the amplification factors of the oscillation equation, numerical experiments performed with a 3D circulation ocean model.

Mots clés: Oscillation equation; Kinetic energy balance; RAW filter; FD filter; TDE filter; TDI filter; Leap Frog; Physical mode; Computational mode; Robert-Asselin filter; Laplacian filter

Domaines: Planète et Univers [physics]; Océan, Atmosphère

Patrick Marsaleix, Francis Auclair, Thomas Duhaut, Claude Estournel, Cyril Nguyen, et al.. Alternatives to the Robert–Asselin filter. Ocean Modelling, 2012, 41, pp.53-66. ⟨10.1016/j.ocemod.2011.11.002⟩. ⟨hal-02110112⟩