Geodesic
Numerical simulation of wave motions on a rotating attracting spherical zone
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 469-487

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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 “ridges” 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. 
@article{ZVMMF_2015_55_3_a10,
     author = {V. V. Ostapenko and A. V. Speshilova and A. A. Cherevko and A. P. Chupakhin},
     title = {Numerical simulation of wave motions on a rotating attracting spherical zone},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {469--487},
     publisher = {mathdoc},
     volume = {55},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a10/}
}
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V. V. Ostapenko; A. V. Speshilova; A. A. Cherevko; A. P. Chupakhin. Numerical simulation of wave motions on a rotating attracting spherical zone. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 3, pp. 469-487. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_3_a10/