Hamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation

The Hamiltonian particle-mesh method for the spherical shallow water equations

The Hamiltonian particle-mesh (HPM) method is generalized to the spherical shallow water equations, utilizing constrained particle dynamics on the sphere and smoothing with Merilees’ double-periodic FFT formulation of O(J log J) in the latitudinal gridsize. The time step for the explicit, symplectic integrator depends only on the uniform smoothing length. 2000 Mathematics Subject Classification...

Hamiltonian Particle - Mesh Method for Two - Layershallow - Water Equations Subject to the Rigid - Lidapproximationcolin

The Repulsive-particle Method and the Symplectic Integration of the Shallow-water Equations

We discuss the numerical implementation of the shallow-water equations in Lag-rangian coordinates. We show that a nite-dimensional Hamiltonian approximation can be obtained based either on a moving grid or on a smooth-particle approach. We introduce a new particle method which, in some sense, combines moving mesh and smooth-particle methods. We show how this new method, which we call the repuls...

1 A Hamiltonian Particle - Mesh Method forthe Rotating Shallow Water

A new particle-mesh method is proposed for the rotating shallow-water equations. The spatially truncated equations are Hamiltonian and satisfy a Kelvin circulation theorem. The generation of non-smooth components in the layer-depth is avoided by applying a smoothing operator similar to what has recently been discussed in the context of-Euler models. The interplay, in atmospheric ows, between hi...

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 paper, 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 com...