Discrete port-Hamiltonian formulation and numerical approximation for systems of two conservation laws
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}
}