To a close approximation, the atmosphere is in a state of geostrophic and hydrostatic balance. For atmospheric flows, departures from geostrophy are approximately linear. The Mach number of these flows is generally much less than one, and shock waves are not present. In this regime, the dynamical character of the fluid is dominated by wave motion. As a result, the correct treatment of linear waves is intrinsic to any accurate approach for modeling the equations of motion.
This talk provides an intercomparison of the dispersive and diffusive properties of several standard numerical methods as applied to the linear wave equation, including upwind and central finite-volume, spectral finite-volume, discontinuous Galerkin, spectral element, and staggered finite-volume. All methods are studied up to tenth-order accuracy, where possible. A consistent framework is developed which allows for direct intercomparison of the ability of these methods to capture the behavior of wave-like motions. The goal of this work is threefold: first, to determine the shortest wavelength which can be considered “resolved” for a particular method; second, to determine the effect of increasing the order of accuracy on the ability of a method to capture wave-like motion; third, to determine which numerical methods offer the best treatment of wave-like motion.