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• W2980406723 abstract "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." @default.
• W2980406723 created "2019-10-25" @default.
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• W2980406723 date "2019-10-15" @default.
• W2980406723 modified "2023-09-27" @default.
• W2980406723 title "A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds" @default.
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