A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere

@article{Flyer2012AGT,
  title={A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere},
  author={Natasha Flyer and Erik Lehto and S{\'e}bastien Blaise and Grady B. Wright and Amik St.-Cyr},
  journal={J. Comput. Physics},
  year={2012},
  volume={231},
  pages={4078-4095}
}
The current paper establishes the computational efficiency and accuracy of the RBFFD method for large-scale geoscience modeling with comparisons to state-of-the-art methods as high-order discontinuous Galerkin and spherical harmonics, the latter using expansions with close to 300,000 bases. The test cases are demanding fluid flow problems on the sphere that exhibit numerical challenges, such as Gibbs phenomena, sharp gradients, and complex vortical dynamics with rapid energy transfer from large… CONTINUE READING
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