Hamiltonian discontinuous Galerkin FEM for linear, stratified (in)compressible Euler equations: internal gravity waves

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• 作者：Alexander M. van Oers^a ; ^{Sander.van.Oers@nioz.nl} ; Leo R.M. Maas^b ; ^a ; Onno Bokhove^c
• 关键词：Linear stratified Euler equations ; Hamiltonian structure ; Discontinuous Galerkin method ; Internal gravity waves ; Wave attractors
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：770-793
• 全文大小：2247 K
• 卷排序：330

文摘

The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and energy. This required (i) the discretization of the Hamiltonian structure using alternating flux functions and symplectic time integration, (ii) the discretization of a divergence-free velocity field using Dirac's theory of constraints and (iii) the handling of large-scale computational demands due to the 3-dimensional nature of internal gravity waves and, in confined, symmetry-breaking fluid domains, possibly its narrow zones of attraction.