### Abstract

We look into the problem of approximating the shallow water equations with Coriolis forces and topography. We model the system as an in��?nite-dimensional port-Hamiltonian system which is represented by a non-constant Stokes-Dirac structure. We here employ the idea of using diﬀerent ��?nite elements for the approximation of geometric variables (forms) describing a distributed parameter system, to spatially discretize the system and obtain a lumped parameter port-Hamiltonian system. The discretized model then captures the physical laws of its infinite-dimensional couterpart such as conservation of energy. We present some preliminary numerical results to justify our claims.

Original language | Undefined |
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Title of host publication | Eighteenth International symposium on Mathematical Theory of Networks and Systems, MTNS 2008 |

Place of Publication | Blacksburg, Virginia, USA |

Publisher | Virginia Tech |

Pages | - |

Number of pages | 15 |

ISBN (Print) | not assigned |

Publication status | Published - 28 Jul 2008 |

Event | 18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008 - Blacksburg, United States Duration: 28 Jul 2008 → 1 Aug 2008 Conference number: 18 |

### Publication series

Name | |
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Publisher | Virginia Tech |

Number | 412 |

### Conference

Conference | 18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008 |
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Abbreviated title | MTNS |

Country | United States |

City | Blacksburg |

Period | 28/07/08 → 1/08/08 |

### Keywords

- MSC-34K35
- Shallow water equations
- Port-Hamiltonian
- METIS-255454
- IR-65342
- Distributed and Lumped Parameter systems
- EWI-14958

## Cite this

Ramkrishna Pasumarthy, R. P., Ambati, V. R., & van der Schaft, A. (2008). Port-Hamiltonian formulation of shallow water equations with Coriolis force and topography. In

*Eighteenth International symposium on Mathematical Theory of Networks and Systems, MTNS 2008*(pp. -). Blacksburg, Virginia, USA: Virginia Tech.