Analysis of a regularized, time-staggered discretization method and its link to the semi-implicit method

A key aspect of the recently proposed Hamiltonian particle-mesh (HPM) method is its time-staggered discretization combined with a regularization of the continuous governing equations. In this article, the time discretization aspect of the HPM method is analysed for the linearized, rotating, shallow-water equations with orography, and the combined effect of time-staggering and regularization is compared analytically with the popular two-time-level semi-implicit time discretization of the unregularized equations. It is found that the two approaches are essentially equivalent, provided the regularization parameter is chosen appropriately in terms of the time step Δ t. The article treats space as a continuum and, hence, its analysis is not limited to the HPM method.