In applications of radial basis functions (RBFs) for fluid modeling, infinitely smooth RBFs have traditionally been used due to their spectral convergence properties. However, fluid flows in nature can exhibit complex features such that spectral accuracy cannot be realized on resolutions that are observable or practical. A novel approach for modeling with RBF-generated finite differences (RBF-FD) is presented by using polyharmonic spline RBFs together with high-order polynomials. The approach is tested on nonhydrostatic compressible atmospheric flows in limited area domains.