This paper investigates a flux-differencing discontinuous Galerkin method for simulating a fully compressible, nonhydrostatic dry atmosphere. The formulation combines high-order accuracy with numerical dissipation that helps control unresolved motion. It is tested on dry atmospheric boundary-layer convection and the Held-Suarez global circulation benchmark. In these experiments, the method remains stable without adding filters, divergence damping, explicit diffusion, hyperdiffusion, or sponge layers. Readers get the numerical formulation and benchmark evidence needed to understand its tradeoff between accuracy and stability in atmospheric modeling.