Towards a geometric variational discretization of compressible fluids: The rotating shallow water equations
File(s)
Accepted version
Author(s)
Bauer, Werner
Gay-Balmaz, François
Type
Journal Article
Abstract
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Our framework applies to irregular mesh discretizations in 2D and 3D. It systematically extends work previously made for incompressible fluids to the compressible case. We consider in detail the numerical scheme on 2D irregular simplicial meshes and evaluate the scheme numerically for the rotating shallow water equations. In particular, we investigate whether the scheme conserves stationary solutions, represents well the nonlinear dynamics, and approximates well the frequency relations of the continuous equations, while preserving conservation laws such as mass and total energy.
Date Issued
2019-06-01
Date Acceptance
2018-11-22
Citation
Journal of Computational Dynamics, 2019, 6 (1), pp.1-37
ISSN
2158-2505
Publisher
American Institute of Mathematical Sciences (AIMS)
Start Page
1
End Page
37
Journal / Book Title
Journal of Computational Dynamics
Volume
6
Issue
1
Copyright Statement
© 2021 American Institute of Mathematical Sciences.
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Geometric discretization
structure-preserving schemes
fluid dynamics
Euler-Poincare formulation
rotating shallow water equations
PART I
LIE
SUPERCONVERGENCE
INTEGRATORS
DYNAMICS
math.NA
math.NA
physics.comp-ph
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
Publication Status
Published