Geodesic
A finite-volume TVD Riemann solver for the 2D shallow water equations
Numerical methods and programming, Tome 7 (2006) no. 1, pp. 108-112

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A finite-volume numerical scheme for the initial-boundary value problem with evolutionary 2D shallow water equations is proposed. Contact discontinuities are represented by the approximate Riemann condition. The proposed numerical scheme is adopted to solve the dry-cell problems for dam-break cases. Nonlinear parts of equations are represented by the TVD MUSCL (Total Variation Diminishing, Monotonic Upstream Scheme for Conservation Laws) scheme that preserves monotony and high accuracy in the computational domain.
Keywords: finite-volume schemes, shallow water equation, total variation diminishing algorithm, upstream schemes. 
@article{VMP_2006_7_1_a12,
     author = {N. M. Evstigneev},
     title = {A finite-volume {TVD} {Riemann} solver for the {2D} shallow water equations},
     journal = {Numerical methods and programming},
     pages = {108--112},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2006_7_1_a12/}
}
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N. M. Evstigneev. A finite-volume TVD Riemann solver for the 2D shallow water equations. Numerical methods and programming, Tome 7 (2006) no. 1, pp. 108-112. http://geodesic.mathdoc.fr/item/VMP_2006_7_1_a12/