The f-wave Riemann Solver for Meso- and Micro-Scale Flows

Abstract

The design and implementation of the f-wave approximate Riemann solver for timedependent, three-dimensional mesoand micro-scale atmospheric flows is described in detail. The resulting finite volume scheme is conservative and has the ability to resolve regions of steep gradients accurately. Positivity of scalars is also guaranteed by applying the total variation diminishing (TVD) condition appropriately. The Riemann solver employs flux-based wave decomposition (f-waves) for the calculation of Godunov fluxes and does not require the explicit definition of the Roe matrix to enforce conservation. This is an important property in the context of atmospheric flows since the Roe matrix for hyperbolic conservation laws governing atmospheric flows cannot be constructed. The other important feature of the Riemann solver is its ability to incorporate source term due to gravity without introducing discretization errors. Again, in the context of atmospheric flows this is an important advantage. In addition, the scheme requires no explicit filtering or grid staggering for stability. To the best of author’s knowledge, this is the first implementation of a Godunov-type scheme for mesoand micro-scale atmospheric flows in three dimensions.