### Abstract

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

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 48 |

State | Published - Dec 2011 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1970 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Fingerprint

### Keywords

- IR-79126
- METIS-284943
- EWI-21124
- Hamiltonian structure
- Discontinuous Galerkin method
- Compatible schemes
- Linear Euler equations
- Inertial waves

### Cite this

*Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves*. (Memorandum / Department of Applied Mathematics; No. 1970). Enschede: University of Twente, Department of Applied Mathematics.

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*Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves*. Memorandum / Department of Applied Mathematics, no. 1970, University of Twente, Department of Applied Mathematics, Enschede.

**Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves.** / Nurijanyan, S.; van der Vegt, Jacobus J.W.; Bokhove, Onno.

Research output: Professional › Report

TY - BOOK

T1 - Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves

AU - Nurijanyan,S.

AU - van der Vegt,Jacobus J.W.

AU - Bokhove,Onno

PY - 2011/12

Y1 - 2011/12

N2 - A discontinuous Galerkin nite element method (DGFEM) has been developed and tested for linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions. The numerical challenges concern: (i) discretisation of a divergence-free velocity eld; (ii) discretisation of geostrophic boundary conditions combined with no-normal ﬂow at solid walls; (iii) discretisation of the conserved, Hamiltonian dynamics of the inertial-waves; and, (iv) large-scale computational demands owing to the three-dimensional nature of inertial-wave dynamics and possibly its narrow zones of chaotic attraction. These issues have been resolved: (i) by employing Dirac’s method of constrained Hamiltonian dynamics to our DGFEM for linear, compressible ﬂows, thus enforcing the incompressibility constraints; (ii) by enforcing no-normal ﬂow at solid walls in a weak form and geostrophic tangential ﬂow —along the wall; (iii) by applying a symplectic time discretisation; and, (iv) by combining PETSc’s linear algebra routines with our high-level software. We compared our simulations with exact solutions of three-dimensional compressible and incompressible ﬂows, in (non)rotating periodic and partly periodic cuboids (Poincar´e waves). Additional verications concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls.

AB - A discontinuous Galerkin nite element method (DGFEM) has been developed and tested for linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions. The numerical challenges concern: (i) discretisation of a divergence-free velocity eld; (ii) discretisation of geostrophic boundary conditions combined with no-normal ﬂow at solid walls; (iii) discretisation of the conserved, Hamiltonian dynamics of the inertial-waves; and, (iv) large-scale computational demands owing to the three-dimensional nature of inertial-wave dynamics and possibly its narrow zones of chaotic attraction. These issues have been resolved: (i) by employing Dirac’s method of constrained Hamiltonian dynamics to our DGFEM for linear, compressible ﬂows, thus enforcing the incompressibility constraints; (ii) by enforcing no-normal ﬂow at solid walls in a weak form and geostrophic tangential ﬂow —along the wall; (iii) by applying a symplectic time discretisation; and, (iv) by combining PETSc’s linear algebra routines with our high-level software. We compared our simulations with exact solutions of three-dimensional compressible and incompressible ﬂows, in (non)rotating periodic and partly periodic cuboids (Poincar´e waves). Additional verications concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls.

KW - IR-79126

KW - METIS-284943

KW - EWI-21124

KW - Hamiltonian structure

KW - Discontinuous Galerkin method

KW - Compatible schemes

KW - Linear Euler equations

KW - Inertial waves

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves

PB - University of Twente, Department of Applied Mathematics

ER -