Hamiltonian particle‐mesh simulations for a non‐hydrostatic vertical slice model

Abstract

AbstractA Lagrangian particle method is developed for the simulation of atmospheric flows in a non‐hydrostatic vertical slice model. The proposed particle method is an extension of the Hamiltonian particle mesh (HPM) [Frank J, Gottwald G, Reich S. 2002. The Hamiltonian particle‐mesh method. In Meshfree Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, Vol. 26, Griebel M, Schweitzer M (eds). Springer‐Verlag: Berlin Heidelberg; 131–142] and provides preservation of mass, momentum, and energy. We tested the method for the gravity wave test in Skamarock W, Klemp J. 1994. Efficiency and accuracy of the Klemp‐Wilhelmson time‐splitting technique. Monthly Weather Review 122: 2623–2630 and the bubble experiments in Robert A. 1993. Bubble convection experiments with a semi‐implicit formulation of the Euler equations. Journal of the Atmospheric Sciences 50: 1865–1873. The accuracy of the solutions from the HPM simulation is comparable to those reported in these references. A particularly appealing aspect of the method is in its non‐diffusive transport of potential temperature. The solutions are maintained smooth largely due to a ‘regularization’ of pressure, which is controlled carefully to preserve the total energy and the time‐reversibility of the model. In case of the bubble experiments, one also needs to regularize the buoyancy contributions. The simulations demonstrate that particle methods are potentially applicable to non‐hydrostatic atmospheric flow regimes and that they lead to a highly accurate transport of materially conserved quantities such as potential temperature under adiabatic flow regimes. Copyright © 2009 Royal Meteorological Society