A high-resolution numerical method for solving the shallow water equations based on the modified CABARET scheme
https://doi.org/10.25587/SVFU.2023.33.65.009
Abstract
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.
About the Authors
D. G. Asfandiyarov
Nuclear Safety Institute of Russian Academy of Sciences
Russian Federation
Russian Federation
Danil G. Asfandiyarov
52 Bolshaya Tulskaya Street, 115191 Moscow, Russia
O. S. Sorokovikova
Nuclear Safety Institute of Russian Academy of Sciences
Russian Federation
Russian Federation
Olga S. Sorokovikova
52 Bolshaya Tulskaya Street, 115191 Moscow, Russia
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Review
For citations:
Asfandiyarov D.G., Sorokovikova O.S. A high-resolution numerical method for solving the shallow water equations based on the modified CABARET scheme. Mathematical notes of NEFU. 2023;30(3):91-112. (In Russ.) https://doi.org/10.25587/SVFU.2023.33.65.009
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