Improved second-order hyperbolic residual-distribution scheme and its extension to third-order on arbitrary triangular grids

@article{Mazaheri2015ImprovedSH,
  title={Improved second-order hyperbolic residual-distribution scheme and its extension to third-order on arbitrary triangular grids},
  author={Alireza Mazaheri and Hiroaki Nishikawa},
  journal={J. Comput. Physics},
  year={2015},
  volume={300},
  pages={455-491}
}
In this paper, we construct second- and third-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the accuracy of the second-order hyperbolic schemes in J. Comput. Phys. 227 (2007) 315-352 and J. Comput. Phys. 229 (2010) 3989-4016 can be greatly improved by requiring the scheme to preserve exact quadratic solutions. The improved second-order scheme can be easily extended to a third-order scheme by further… CONTINUE READING

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