Alternatives to the Robert–Asselin filter

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.

► The Laplacian time filter of Marsaleix et al. (2008) is compared to the Robert–Asselin filter. ► The discrete kinetic energy balance enlightens on the behaviour of different time filters. ► High order time filters enable to damp the computational mode with no diffusive effect on the physical mode. ► The phase errors remain the weak point of the Leap Frog time stepping scheme.