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 time using a variant of the symplectic SHAKE/RATTLE algorithm. It is demonstrated that the elimination of external gravity waves by the rigid-lid approximation can be achieved in a computationally stable and efficient way.
particle methods, rotating shallow-water equations, symplectic integration, rigid-lid approximation
Particle methods and lattice-gas methods (msc 76M28)
SIAM Journal on Applied Dynamical Systems
Computational Dynamics

Cotter, C.J, Frank, J.E, & Reich, S. (2004). Hamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation. SIAM Journal on Applied Dynamical Systems, 3(1), 69–83. doi:10.1137/030600076