A fully Lagrangian constrained hydrostatic method for atmospheric flows

The hydrostatic primitive equations of motion, which have been used in large-scale weather prediction over the last decades, are considered within a Lagrangian framework. This model is discretized by extending the Hamiltonian Particle-Mesh method of Gottwald et al. (2002), in which the particles represent large masses of fluid. The new model is a 2D hydrostatic one full ideal fluid equations in potential temperature function formulation, such that the particle motion is constrained to preserve a hydrostatic state. The spatial truncation is (at least locally) Hamiltonian, making integration with a symplectic method appropriate. A code for studying the air flow in the atmosphere was made and successfully tested for a two-dimensional problem.