ENERGY-STABLE AND LINEARLY WELL-BALANCED NUMERICAL SCHEMES FOR THE NONLINEAR SHALLOW WATER EQUATIONS WITH THE CORIOLIS FORCE

被引：0

作者：

Audusse, Emmanuel ^{[1
]}

Dubos, Virgile ^{[2
]}

Gaveau, Noemie ^{[3
]}

Penel, Yohan ^{[4
]}

机构：

[1] Universite, Inst Galile, LAGA, Sorbonne Paris Nord, F-93430 Villetaneuse, France

[2] Inst Polytech Paris, POEMS, INRIA, ENSTA Paris,CNRS, F-91120 Palaiseau, France

[3] Univ Orleans, Univ Tours, Inst Denis Poisson, CNRS UMR, F-45067 Orleans, France

[4] Sorbonne Univ, INRIA Paris, CNRS JLLteam ANGE, F-75589 Paris, France

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2025年 / 47卷 / 01期

关键词：

shallow water equations; Coriolis force; well-balanced schemes; colocated finite- volume schemes; energy-decreasing schemes; GEOSTROPHIC ADJUSTMENT; TERM;

D O I：

10.1137/22M1515707

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze a class of energy-stable and linearly well-balanced numerical schemes dedicated to the nonlinear shallow water equations with the Coriolis force. The proposed algorithms rely on colocated finite-difference approximations formulated on Cartesian geometries. They involve appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic equilibrium. We show that the resulting methods ensure semidiscrete energy estimates. Among the proposed algorithms, a colocated finite-volume scheme is described. Numerical results show a very clear improvement around the nonlinear geostrophic equilibrium when compared to those of classic Godunov-type schemes.

引用

页码：A1 / A23

页数：23

共 29 条

[1]

Audusse E., 2021, ESAIM: Proceedings and Surveys, V70, P31, DOI [10.1051/proc/202107003, 10.1051/proc/202107003]

[2] Conservative discretization of Coriolis force in a finite volume framework [J].

Audusse, E. ;

Klein, R. ;

Owinoh, A. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (08) :2934-2950

[3] Analysis of modified Godunov type schemes for the two-dimensional linear wave equation with Coriolis source term on cartesian meshes [J].

Audusse, Emmanuel ;

Do Minh Hieu ;

Omnes, Pascal ;

Penel, Yohan .

JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 373 :91-129

[4] UPWIND METHODS FOR HYPERBOLIC CONSERVATION-LAWS WITH SOURCE TERMS [J].

BERMUDEZ, A ;

VAZQUEZ, E .

COMPUTERS & FLUIDS, 1994, 23 (08) :1049-1071

[5]

BERTHON C., 2020, Int. J. Finite, V15

[6] Frontal geostrophic adjustment and nonlinear wave phenomena in one-dimensional rotating shallow water. Part 2. High-resolution numerical simulations [J].

Bouchut, F ;

Le Sommer, J ;

Zeitlin, V .

JOURNAL OF FLUID MECHANICS, 2004, 514 :35-63

[7]

Bouchut F., 2004, NONLINEAR STABILITY, DOI DOI 10.1007/B93802

[8] FINITE VOLUME SIMULATION OF THE GEOSTROPHIC ADJUSTMENT IN A ROTATING SHALLOW-WATER SYSTEM [J].

Castro, Manuel J. ;

Antonio Lopez, Juan ;

Pares, Carlos .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2008, 31 (01) :444-477

[9] Well-balanced schemes for the shallow water equations with Coriolis forces [J].

Chertock, Alina ;

Dudzinski, Michael ;

Kurganov, Alexander ;

Lukacova-Medvid'ova, Maria .

NUMERISCHE MATHEMATIK, 2018, 138 (04) :939-973

[10] An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification [J].

Couderc, F. ;

Duran, A. ;

Vila, J. -P. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 343 :235-270

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