A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics

An explicit finite-volume solver is proposed for numerical simulation of non-hydrostatic atmospheric dynamics with promise for efficiency on massively parallel machines via low communication needs and large time steps. Solving the governing equations with a single stage lowers communication, and using the method of characteristics to follow information as it propagates enables large time steps. Using a non-oscillatory interpolant, the method is stable without post-hoc filtering. Characteristic variables (built from interface flux vectors) are integrated upstream from interfaces along their trajectories to compute time-averaged fluxes over a time step. Thus we call this method a Flux-Based Characteristic Semi-Lagrangian (FBCSL) method. Multidimensionality is achieved via a second-order accurate Strang operator splitting. Spatial accuracy is achieved via the third- to fifth-order accurate Weighted Essentially Non-Oscillatory (WENO) interpolant. We implement the theory to form a 2-D non-hydrostatic compressible (Euler system) atmospheric model in which standard test cases confirm accuracy and stability. We maintain stability with time steps larger than CFL = 1 (CFL number determined by the acoustic wave speed, not advection) but note that accuracy degrades unacceptably for most cases with CFL > 2. For the smoothest test case, we ran out to CFL = 7 to investigate the error associated with simulation at large CFL number time steps. Analysis suggests improvement of trajectory computations will improve error for large CFL numbers. (C) 2010 Elsevier Inc. All rights reserved.