Port-Hamiltonian formulation of shallow water equations with Coriolis force and topography

R.P. Ramkrishna Pasumarthy, V.R. Ambati, Arjan van der Schaft

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    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 languageUndefined
    Title of host publicationEighteenth International symposium on Mathematical Theory of Networks and Systems, MTNS 2008
    Place of PublicationBlacksburg, Virginia, USA
    PublisherVirginia Tech
    Pages-
    Number of pages15
    ISBN (Print)not assigned
    Publication statusPublished - 28 Jul 2008
    Event18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008 - Blacksburg, United States
    Duration: 28 Jul 20081 Aug 2008
    Conference number: 18

    Publication series

    Name
    PublisherVirginia Tech
    Number412

    Conference

    Conference18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008
    Abbreviated titleMTNS
    CountryUnited States
    CityBlacksburg
    Period28/07/081/08/08

    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.