Euler solutions using flux‐based wave decomposition

The Euler equations are solved for non‐hydrostatic atmospheric flow problems in two dimensions using a high‐resolution Godunov‐type scheme. The Riemann problem is solved using a flux‐based wave decomposition suggested by LeVeque. This paper describes in detail, the design and implementation of the Riemann solver used for computing the Godunov fluxes. The methodology is then validated against benchmark cases for non‐hydrostatic atmospheric flows. Comparisons are made with solutions obtained from the National Center for Atmospheric Research's state‐of‐the‐art numerical model. The method shows promise in simulating non‐hydrostatic flows, which are characterized by steep gradients on the meso‐, micro‐ and urban‐scales. Copyright © 2006 John Wiley & Sons, Ltd.