A Godunov-type Finite Volume Scheme for Meso- and Micro-scale Flows in Three Dimensions

Abstract

This short note reports the extension of the f-waves approximate Riemann solver (Ahmad and Lindeman, 2007; LeVeque, 2002; Bale et al., 2002) for three-dimensional meso- and micro-scale atmospheric flows. The Riemann solver employs flux-based wave decomposition for the calculation of Godunov fluxes and does not require the explicit definition of the Roe matrix to enforce conservation. The other important feature of the Riemann solver is its ability to incorporate source term due to gravity without introducing discretization errors. The resulting finite volume scheme is second-order accurate in space and time. The finite-difference schemes currently used in atmospheric flow models are neither conservative nor able to resolve regions of sharp gradients. The finite volume scheme described in this paper is fully conservative and has the ability to resolve regions of sharp gradients without introducing spurious oscillations in the solution. The scheme shows promise in accurately resolving flows on the meso- and micro-scales and should be considered for implementation in the dynamical cores of next generation meso- and micro-scale atmospheric flow models.