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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 3, Pages 469–487 (Mi zvmmf10174)  

Numerical simulation of wave motions on a rotating attracting spherical zone

V. V. Ostapenkoab, A. V. Speshilovaa, A. A. Cherevkoab, A. P. Chupakhinab

a Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent'eva 15, Novosibirsk, 630090, Russia
b Novosibirsk State University, Universitetskii pr. 2, Novosibirsk, 630090, Russia

Abstract: The Riemann problem for the shallow water model on a rotating attracting spherical zone numerically is solved. A shock-capturing difference scheme is constructed that approximates the system of conservation laws describing discontinuous solutions of the given model. The Riemann problem is formulated as one of developing a wave process from initial data representing a spherical zone covered by various equilibria and zonal flows. Two Riemann problems are numerically simulated: the breakdown of water УridgesФ of various shapes at equilibrium and propagation of contact discontinuity perturbations between an equilibrium and a zonal flow. The general properties of such solutions independent of the geometric configuration of the domains occupied by elementary solutions in the initial data are demonstrated.

Key words: conservation laws for shallow water equations on a rotating attracting spherical zone, Riemann problem, equilibrium, zonal flows, shock-capturing difference scheme, decay of ridges in the form of chevrons and elliptic annuli.

DOI: https://doi.org/10.7868/S0044466915030138

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:3, 470–486

Bibliographic databases:

UDC: 519.634
MSC: Primary 65M06; Secondary 86A10
Received: 24.09.2013
Revised: 09.10.2014

Citation: V. V. Ostapenko, A. V. Speshilova, A. A. Cherevko, A. P. Chupakhin, “Numerical simulation of wave motions on a rotating attracting spherical zone”, Zh. Vychisl. Mat. Mat. Fiz., 55:3 (2015), 469–487; Comput. Math. Math. Phys., 55:3 (2015), 470–486

Citation in format AMSBIB
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  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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