A well-balanced central-upwind scheme for the thermal rotating shallow water equations

Kurganov，Alexander1,2; Liu，Yongle1,3; Zeitlin，Vladimir1,4

2020-06-15

10.1016/j.jcp.2020.109414

JOURNAL OF COMPUTATIONAL PHYSICS   影响因子和分区

0021-9991

1090-2716

We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients—the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization approach: first, the source terms are incorporated into the fluxes, which results in a hyperbolic system with global fluxes; second, we apply the Riemann-problem-solver-free central-upwind scheme to the rewritten system. We ensure that the resulting method is well-balanced by switching off the numerical diffusion when the computed solution is near (at) thermo-geostrophic equilibria. The designed scheme is successfully tested on a series of numerical examples. Motivated by future applications to large-scale motions in the ocean and atmosphere, the model is considered on the tangent plane to a rotating planet both in mid-latitudes and at the Equator. The numerical scheme is shown to be capable of quite accurately maintaining the equilibrium states in the presence of nontrivial topography and rotation. Prior to numerical simulations, an analysis of the TRSW model based on the use of Lagrangian variables is presented, allowing one to obtain criteria of existence and uniqueness of the equilibrium state, of the wave-breaking and shock formation, and of instability development out of given initial conditions. The established criteria are confirmed in the conducted numerical experiments.

Central-upwind scheme Flux globalization Steady-state solutions (equilibria) Thermal rotating shallow water equations Thermo-geostrophic equilibria Well-balanced method

SCI ; EI

英语

第一 ; 通讯

NSFC[11771201] ; fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]

Computer Science ; Physics

Computer Science, Interdisciplinary Applications ; Physics, Mathematical

WOS:000534235200002

ACADEMIC PRESS INC ELSEVIER SCIENCE

20201708549611

Equations of motion ; Horizontal wells ; Astrophysics ; Topography

Oil Fields:512.1.1 ; Extraterrestrial Physics and Stellar Phenomena:657.2 ; Calculus:921.2 ; Numerical Methods:921.6 ; Materials Science:951

PHYSICS

2-s2.0-85082188733

Scopus

1.Department of Mathematics,Southern University of Science and Technology,Shenzhen,518055,China
2.SUSTech International Center for Mathematics,Southern University of Science and Technology,Shenzhen,518055,China
3.Department of Mathematics,Harbin Institute of Technology,Harbin,150001,China
4.Laboratoire de Météorologie Dynamique,Sorbonne Université (SU),Ecole Normale Supérieure (ENS),CNRS,Paris,75231,France

Kurganov，Alexander,Liu，Yongle,Zeitlin，Vladimir. A well-balanced central-upwind scheme for the thermal rotating shallow water equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2020,411.

Kurganov，Alexander,Liu，Yongle,&Zeitlin，Vladimir.(2020).A well-balanced central-upwind scheme for the thermal rotating shallow water equations.JOURNAL OF COMPUTATIONAL PHYSICS,411.

Kurganov，Alexander,et al."A well-balanced central-upwind scheme for the thermal rotating shallow water equations".JOURNAL OF COMPUTATIONAL PHYSICS 411(2020).