The Hamiltonian particle-mesh method for the spherical shallow water equations
نویسندگان
چکیده
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: 65M99, 86A10
منابع مشابه
Hamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation
We develop a particle-mesh method for two-layer shallow-water equations subject to the rigid-lid approximation. The method is based on the recently proposed Hamiltonian particle-mesh (HPM) method and the interpretation of the rigid-lid approximation as a set of holonomic constraints. The suggested spatial discretization leads to a constrained Hamiltonian system of ODEs which is integrated in ti...
متن کامل1 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...
متن کاملThe 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...
متن کاملAnalysis 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...
متن کاملConvergence of the Hamiltonian particle-mesh method for barotropic fluid flow
We prove convergence of the Hamiltonian Particle-Mesh (HPM) method, initially proposed by J. Frank, G. Gottwald, and S. Reich, on a periodic domain when applied to the irrotational shallow water equations as a prototypical model for barotropic compressible fluid flow. Under appropriate assumptions, most notably sufficiently fast decay in Fourier space of the global smoothing operator, and a Str...
متن کامل