Geodesic
Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 170-184

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Regularized shallow water equations are derived as based on a regularization of the Navier–Stokes equations in the form of quasi-gasdynamic and quasi-hydrodynamic equations. Efficient finite-difference algorithms based on the regularized shallow water equations are proposed for the numerical simulation of shallow water flows. The capabilities of the model are examined by computing a test Riemann problem, the flow over an obstacle, and asymmetric dam break. 
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O. V. Bulatov; T. G. Elizarova. Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 170-184. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a12/