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.
|Title of host publication||Eighteenth International symposium on Mathematical Theory of Networks and Systems, MTNS 2008|
|Place of Publication||Blacksburg, Virginia, USA|
|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
|Conference||18th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2008|
|Period||28/07/08 → 1/08/08|
- Shallow water equations
- Distributed and Lumped Parameter systems
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.