Geodesic
A high-resolution numerical method for solving the shallow water equations based on the modified CABARET scheme
Matematičeskie zametki SVFU, Tome 30 (2023) no. 3, pp. 91-112 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical method based on the CABARET scheme for modeling unsteady flow over arbitrary topography in the shallow water approximation is developed. The method allows simulating a wide range of flow conditions, including transcritical. To model transcritical transitions, a hybrid approach is used based on solving the local Riemann problem, as is done in Godunov-type schemes. The presented numerical method has a well-balance condition-the fulfillment of the condition of hydrostatic equilibrium or the condition of a fluid at rest on an uneven bottom topography. A robust technique is used to simulate the movement of wet/dry fronts caused by flooding or recession. A number of physical processes are taken into account, such as bed friction and rain. Numerical results are compared with analytical solutions and data from the dam-break experiment.
Keywords: shallow water equations, balance-characteristic approach, wet/dry fronts, complex topography.
Mots-clés : CABARET scheme 
@article{SVFU_2023_30_3_a7,
     author = {D. G. Asfandiyarov and O. S. Sorokovikova},
     title = {A high-resolution numerical method for solving the shallow water equations based on the modified {CABARET} scheme},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {91--112},
     year = {2023},
     volume = {30},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2023_30_3_a7/}
}
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D. G. Asfandiyarov; O. S. Sorokovikova. A high-resolution numerical method for solving the shallow water equations based on the modified CABARET scheme. Matematičeskie zametki SVFU, Tome 30 (2023) no. 3, pp. 91-112. http://geodesic.mathdoc.fr/item/SVFU_2023_30_3_a7/