Geodesic
Simulation of shallow water flows with shoaling areas and bottom discontinuities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 316-338

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A numerical method based on a second-order accurate Godunov-type scheme is described for solving the shallow water equations on unstructured triangular-quadrilateral meshes. The bottom surface is represented by a piecewise linear approximation with discontinuities, and a new approximate Riemann solver is used to treat the bottom jump. Flows with a dry sloping bottom are computed using a simplified method that admits negative depths and preserves the liquid mass and the equilibrium state. The accuracy and performance of the approach proposed for shallow water flow simulation are illustrated by computing one- and two-dimensional problems. 
@article{ZVMMF_2017_57_2_a8,
     author = {A. I. Aleksyuk and V. V. Belikov},
     title = {Simulation of shallow water flows with shoaling areas and bottom discontinuities},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {316--338},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a8/}
}
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A. I. Aleksyuk; V. V. Belikov. Simulation of shallow water flows with shoaling areas and bottom discontinuities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 2, pp. 316-338. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_2_a8/