  We present a new hyperviscosity formulation for stabilizing radial basis
function-finite difference (RBF-FD) discretizations of
advection-diffusion-reaction equations on manifolds $\mathbb{M} \subset
\mathbb{R}^3$ of co-dimension one. Our technique involves automatic addition of
artificial hyperviscosity to damp out spurious modes in the differentiation
matrices corresponding to surface gradients, in the process overcoming a
technical limitation of a recently-developed Euclidean formulation. Like the
Euclidean formulation, the manifold formulation relies on von Neumann stability
analysis performed on auxiliary differential operators that mimic the spurious
solution growth induced by RBF-FD differentiation matrices. We demonstrate
high-order convergence rates on problems involving surface advection and
surface advection-diffusion. Finally, we demonstrate the applicability of our
formulation to advection-diffusion-reaction equations on manifolds described
purely as point clouds. Our surface discretizations use the recently-developed
RBF-LOI method, and with the addition of hyperviscosity, are now empirically
high-order accurate, stable, and free of stagnation errors.
