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Polyharmonic spline (PHS) radial basis functions (RBFs) are used togetherwith polynomials to create local RBF-finite-difference (RBF-FD) weights ondifferent node layouts for spatial discretization of the compressibleNavier-Stokes equations at low Mach number, relevant to atmospheric flows. Testcases are taken from the numerical weather prediction community and solved onbounded domains. Thus, attention is given on how to handle boundaries with theRBF-FD method, as well as a novel implementation for the presented approach.Comparisons are done on Cartesian, hexagonal, and quasi-uniformly scatterednode layouts. Since RBFs are independent of a coordinate system (and onlydepend on the distance between nodes), changing the node layout amounts tochanging one line of code. In addition, consideration and guidelines are givenon PHS order, polynomial degree and stencil size. The main advantages of thepresent method are: 1) capturing the basic physics of the problem surprisinglywell, even at very coarse resolutions, 2) high-order accuracy without the needof tuning a shape parameter, and 3) the inclusion of polynomials eliminatesstagnation (saturation) errors.

An RBF-FD polynomial method based on polyharmonic splines for the Navier-Stokes equations: Comparisons on different node layouts