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

S. Nurijanyan, Jacobus J.W. van der Vegt, Onno Bokhove

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    Abstract

    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 veri﬿cations concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages48
    Publication statusPublished - Dec 2011

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1970
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

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

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