Authors

Paul Kotyczka, Bernhard Maschke

Abstract

We discuss the discrete formulation of systems of conservation laws in port-Hamiltonian form on dual chain complexes. Based on integral balance equations and topological information, this representation is exact and qualifies as a control model. The finite-dimensional approximation requires an energy discretization that yields discrete constitutive equations. We give (i) a brief overview of discrete modeling of conservation laws on n-complexes and (ii) extend existing results by allowing for mixed physical types of boundary inputs. This requires the construction of a primal and a dual complex based on the underlying staggered grids and the localization of the inputs on the system boundary. Finally, (iii) we discuss the properties of the resulting structure-preserving discretization scheme based on a consistency analysis for the 2D nonlinear shallow water equations.

Citation

  • Journal: at - Automatisierungstechnik
  • Year: 2017
  • Volume: 65
  • Issue: 5
  • Pages: 308–322
  • Publisher: Walter de Gruyter GmbH
  • DOI: 10.1515/auto-2016-0098

BibTeX

@article{Kotyczka_2017,
  title={{Discrete port-Hamiltonian formulation and numerical approximation for systems of two conservation laws}},
  volume={65},
  ISSN={2196-677X},
  DOI={10.1515/auto-2016-0098},
  number={5},
  journal={at - Automatisierungstechnik},
  publisher={Walter de Gruyter GmbH},
  author={Kotyczka, Paul and Maschke, Bernhard},
  year={2017},
  pages={308--322}
}

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