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 but note that accuracy degrades unacceptably for most case with CFL > 2. For the smoothest test case, we ran out to CFL=7 to investigate the error associated with simulation at large CFL time steps. Analysis suggests improvement of trajectory computations will improve error for large CFL numbers.