### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | Toegepaste Wiskunde |

ISBN (Print) | 169-2690 |

Publication status | Published - 2005 |

### Publication series

Name | Memoranda |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1787 |

ISSN (Print) | 0169-2690 |

### Keywords

- EWI-3607
- METIS-227276
- IR-65971
- MSC-35M10
- MSC-65M15

### Cite this

*A (Dis)continuous finite element model for generalized 2D vorticity dynamics*. (Memoranda; No. 1787). Enschede: Toegepaste Wiskunde.

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*A (Dis)continuous finite element model for generalized 2D vorticity dynamics*. Memoranda, no. 1787, Toegepaste Wiskunde, Enschede.

**A (Dis)continuous finite element model for generalized 2D vorticity dynamics.** / Bernsen, E.; Bokhove, Onno; van der Vegt, Jacobus J.W.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - A (Dis)continuous finite element model for generalized 2D vorticity dynamics

AU - Bernsen, E.

AU - Bokhove, Onno

AU - van der Vegt, Jacobus J.W.

N1 - Imported from MEMORANDA

PY - 2005

Y1 - 2005

N2 - A mixed continuous and discontinuous Galerkin finite element discretization is constructed for a generalized vorticity streamfunction formulation in two spatial dimensions. This formulation consists of a hyperbolic (potential) vorticity equation and a linear elliptic equation for a (transport) streamfunction. The generalized formulation includes three systems in geophysical fluid dynamics: the incompressible Euler equations, the barotropic quasi-geostrophic equations and the rigid-lid equations. Multiple connected domains are considered with impenetrable and curved boundaries such that the circulation at each connected piece of boundary must be introduced. The generalized system is shown to globally conserve energy and weighted smooth functions of the vorticity. In particular, the weighted square vorticity or enstrophy is conserved. By construction, the spatial finite-element discretization is shown to conserve energy and is $L^2$-stable in the enstrophy norm. The method is verified by numerical experiments which support our error estimates. Particular attention is paid to match the continuous and discontinuous discretization. Hence, the implementation with a third-order Runge-Kutta time discretization conserves energy and is $L^2$-stable in the enstrophy norm for increasing time resolution in multiple connected curved domains.

AB - A mixed continuous and discontinuous Galerkin finite element discretization is constructed for a generalized vorticity streamfunction formulation in two spatial dimensions. This formulation consists of a hyperbolic (potential) vorticity equation and a linear elliptic equation for a (transport) streamfunction. The generalized formulation includes three systems in geophysical fluid dynamics: the incompressible Euler equations, the barotropic quasi-geostrophic equations and the rigid-lid equations. Multiple connected domains are considered with impenetrable and curved boundaries such that the circulation at each connected piece of boundary must be introduced. The generalized system is shown to globally conserve energy and weighted smooth functions of the vorticity. In particular, the weighted square vorticity or enstrophy is conserved. By construction, the spatial finite-element discretization is shown to conserve energy and is $L^2$-stable in the enstrophy norm. The method is verified by numerical experiments which support our error estimates. Particular attention is paid to match the continuous and discontinuous discretization. Hence, the implementation with a third-order Runge-Kutta time discretization conserves energy and is $L^2$-stable in the enstrophy norm for increasing time resolution in multiple connected curved domains.

KW - EWI-3607

KW - METIS-227276

KW - IR-65971

KW - MSC-35M10

KW - MSC-65M15

M3 - Report

SN - 169-2690

T3 - Memoranda

BT - A (Dis)continuous finite element model for generalized 2D vorticity dynamics

PB - Toegepaste Wiskunde

CY - Enschede

ER -