Abstract
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.
Original language | English |
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Pages (from-to) | 97-104 |
Number of pages | 8 |
Journal | Atmospheric Science Letters |
Volume | 6 |
Issue number | 2 |
DOIs | |
Publication status | Published - Apr 2005 |
Externally published | Yes |
Keywords
- Hamiltonian particle-mesh method
- Leapfrog time-stepping
- Numerical dispersion
- Rotating linear shallow-water equations
- Semi-implicit method