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Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations

Summary: Hamiltonian discontinuous Galerkin FEM for
linear, rotating incompressible Euler equations:
inertial waves
S. Nurijanyan, J.J.W. van der Vegt, O. Bokhove
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE,
Enschede, The Netherlands
A discontinuous Galerkin finite element method (DGFEM) has been de-
veloped and tested for linear, three-dimensional, rotating incompressible Eu-
ler equations. These equations admit complicated wave solutions.
The numerical challenges concern: (i) discretisation of a divergence-free
velocity field; (ii) discretisation of geostrophic boundary conditions combined
with no-normal flow at solid walls; (iii) discretisation of the conserved, Hamil-
tonian 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 dy-
namics 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


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering