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A Radial Basis Function Partition Of Unity Method For Transport On The Sphere, Kevin Aiton
A Radial Basis Function Partition Of Unity Method For Transport On The Sphere, Kevin Aiton
Boise State University Theses and Dissertations
The transport phenomena dominates geophysical fluid motions on all scales making the numerical solution of the transport problem fundamentally important for the overall accuracy of any fluid solver. In this thesis, we describe a new high-order, computationally efficient method for numerically solving the transport equation on the sphere. This method combines radial basis functions (RBFs) and a partition of unity method (PUM). The method is mesh-free, allowing near optimal discretization of the surface of the sphere, and is free of any coordinate singularities. The basic idea of the method is to start with a set of nodes that are quasi-uniformly …