Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws

Authors

Abstract

A reduction method is presented for systems of conservation laws with boundary energy flow. It is stated as a generalized pseudo-spectral method which performs exact differentiation by using simultaneously several approximation spaces generated by polynomials bases and suitable choices of port-variables. The symplecticity of this spatial reduction method is proved when used for the reduction of both closed and open systems of conservation laws, for any choice of collocation points (i.e. for any polynomial bases). The symplecticity of some more usual collocation schemes is discussed and finally their accuracy on approximation of the spectrum, on the example of the ideal transmission line, is discussed in comparison with the suggested reduction scheme.

Keywords

Symplectic methods; Spatial reduction; Pseudo-spectral methods; Hamiltonian systems; Dirac structures; Systems of conservation laws; Open systems

Citation

Journal: Journal of Computational Physics
Year: 2012
Volume: 231
Issue: 4
Pages: 1272–1292
Publisher: Elsevier BV
DOI: 10.1016/j.jcp.2011.10.008

BibTeX

@article{Moulla_2012,
  title={{Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws}},
  volume={231},
  ISSN={0021-9991},
  DOI={10.1016/j.jcp.2011.10.008},
  number={4},
  journal={Journal of Computational Physics},
  publisher={Elsevier BV},
  author={Moulla, R. and Lefévre, L. and Maschke, B.},
  year={2012},
  pages={1272--1292}
}

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