TY - GEN
T1 - Multisymplectic Variational Integrators for Fluid Models with Constraints
AU - Demoures, François
AU - Gay-Balmaz, François
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for barotropic and incompressible fluid models, which satisfy a discrete version of Noether theorem. We show how the geometric integrator can handle regular fluid motion in vacuum with free boundaries and constraints such as the impact against an obstacle of a fluid flowing on a surface. Our approach is applicable to a wide range of models including the Boussinesq and shallow water models, by appropriate choice of the Lagrangian.
AB - We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for barotropic and incompressible fluid models, which satisfy a discrete version of Noether theorem. We show how the geometric integrator can handle regular fluid motion in vacuum with free boundaries and constraints such as the impact against an obstacle of a fluid flowing on a surface. Our approach is applicable to a wide range of models including the Boussinesq and shallow water models, by appropriate choice of the Lagrangian.
KW - Barotropic fluid
KW - Incompressible ideal fluid
KW - Multisymplectic integrator
KW - Noether theorem
KW - Structure preserving discretization
UR - https://www.scopus.com/pages/publications/85112571226
U2 - 10.1007/978-3-030-80209-7_32
DO - 10.1007/978-3-030-80209-7_32
M3 - Conference contribution
AN - SCOPUS:85112571226
SN - 9783030802080
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 283
EP - 291
BT - Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer Science and Business Media Deutschland GmbH
T2 - 5th International Conference on Geometric Science of Information, GSI 2021
Y2 - 21 July 2021 through 23 July 2021
ER -