Convergence Analysis of the Energy and Helicity Preserving Scheme for Axisymmetric Flows

Jian-Guo Liu University of Maryland Wei-Cheng Wang National Tsing Hua University

Numerical Analysis and Scientific Computing mathscidoc:1702.25041

SIAM Journal on Numerical Analysis, 44, (6), 2456-2480, 2006.6
We give an error estimate for the energy and helicity preserving scheme (EHPS) in second order finite difference setting on axisymmetric incompressible flows with swirling velocity. This is accomplished by a weighted energy estimate, along with careful and nonstandard local truncation error analysis near the geometric singularity and a far field decay estimate for the stream function. A key ingredient in our a priori estimate is the permutation identities associated with the Jacobians, which are also a unique feature that distinguishes EHPS from standard finite difference schemes.
incompressible viscous flow, Navier–Stokes equation, pole singularity, conservative scheme, Jacobian, permutation identity, geometric singularity
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@inproceedings{jian-guo2006convergence,
  title={Convergence Analysis of the Energy and Helicity Preserving Scheme for Axisymmetric Flows},
  author={Jian-Guo Liu, and Wei-Cheng Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209091259423469361},
  booktitle={SIAM Journal on Numerical Analysis},
  volume={44},
  number={6},
  pages={2456-2480},
  year={2006},
}
Jian-Guo Liu, and Wei-Cheng Wang. Convergence Analysis of the Energy and Helicity Preserving Scheme for Axisymmetric Flows. 2006. Vol. 44. In SIAM Journal on Numerical Analysis. pp.2456-2480. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209091259423469361.
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