Current community models in the geosciences employ a variety of numerical methods from finite-difference, finite-volume, finite- or spectral elements, to pseudospectral methods. All have specialized strengths but also serious weaknesses. The first three methods are generally considered low-order and can involve high algorithmic complexity (as in triangular elements or unstructured meshes). Global spectral methods do not practically allow for local mesh refinement and often involve cumbersome algebra. Radial basis functions have the advantage of being spectrally accurate for arbitrary node layouts in multi-dimensions with extreme algorithmic simplicity, and naturally permits local node refinement. We will show test examples ranging from vortex roll-ups, modeling idealized cyclogenesis, to the unsteady nonlinear flows posed by the shallow water equations to 3-D mantle convection in the earth’s interior.