Variational integrator for the rotating shallow-water equations on the sphere

被引：16

作者：

Brecht, Rudiger ^{[1
]}

Bauer, Werner ^{[2
]}

Bihlo, Alexander ^{[1
]}

Gay-Balmaz, Francois ^{[3
]}

MacLachlan, Scott ^{[1
]}

机构：

[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

[2] Imperial Coll London, Dept Math, London, England

[3] Ecole Normale Super, CNRS, Lab Meteorol Dynam, Paris, France

来源：

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY | 2019年 / 145卷 / 720期

基金：

加拿大自然科学与工程研究理事会; 欧盟地平线“2020”;

关键词：

rotating shallow-water equations; structure-preserving discretization; variational integrator on sphere; POTENTIAL ENSTROPHY; NUMERICAL-INTEGRATION; DISCRETIZATION; SCHEMES; ENERGY;

D O I：

10.1002/qj.3477

中图分类号：

P4 [大气科学（气象学）];

学科分类号：

0706 ; 070601 ;

摘要：

We develop a variational integrator for the shallow-water equations on a rotating sphere. The variational integrator is built around a discretization of the continuous Euler-Poincare reduction framework for Eulerian hydrodynamics. We describe the discretization of the continuous Euler-Poincare equations on arbitrary simplicial meshes. Standard numerical tests are carried out to verify the accuracy and excellent conservational properties of the discrete variational integrator.

引用

页码：1070 / 1088

页数：19

共 38 条

[11]

Blanes S., 2016, CONCISE INTRO GEOMET, V23

[12] Hamilton-Pontryagin Integrators on Lie Groups Part I: Introduction and Structure-Preserving Properties [J].

Bou-Rabee, Nawaf ;

Marsden, Jerrold E. .

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 2009, 9 (02) :197-219

[13] Symmetry-adapted moving mesh schemes for the nonlinear Schrodinger equation [J].

Budd, C ;

Dorodnitsyn, V .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (48) :10387-10400

[14] VARIATIONAL DISCRETIZATION FOR ROTATING STRATIFIED FLUIDS [J].

Desbrun, Mathieu ;

Gawlik, Evan S. ;

Gay-Balmaz, Francois ;

Zeitlin, Vladimir .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2014, 34 (02) :477-509

[15] Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods - Part 1: Derivation and properties [J].

Eldred, Christopher ;

Randall, David .

GEOSCIENTIFIC MODEL DEVELOPMENT, 2017, 10 (02) :791-810

[16] A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere [J].

Flyer, Natasha ;

Lehto, Erik ;

Blaise, Sebastien ;

Wright, Grady B. ;

St-Cyr, Amik .

JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (11) :4078-4095

[17] A radial basis function method for the shallow water equations on a sphere [J].

Flyer, Natasha ;

Wright, Grady B. .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2009, 465 (2106) :1949-1976

[18]

Frank J, 2003, LECT NOTES COMP SCI, V26, P131

[19] Geometric, variational discretization of continuum theories [J].

Gawlik, E. S. ;

Mullen, P. ;

Pavlov, D. ;

Marsden, J. E. ;

Desbrun, M. .

PHYSICA D-NONLINEAR PHENOMENA, 2011, 240 (21) :1724-1760

[20]

Hairer E., 2006, Structure-Preserving Algorithms for Ordinary Differential Equations, V2nd

← 1 2 3 4 →