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

CY - Enschede

ER -