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. The design and implementation of the Riemann solver used for computing the Godunov fluxes is discussed in detail. The methodology is then validated against benchmark cases for nonhydrostatic atmospheric flows. Comparisons are made with solutions obtained from the National Center for Atmospheric Research's state-of-the-art numerical model (ARW-WRF). The method shows promise in simulating non-hydrostatic flows on the meso-, micro-, and urban-scales, which are characterized by steep gradients.