Abstract
This paper describes the numerical scheme of the one-dimensional Exner - shallow water equations for sediment modeling. Here, our novel numerical scheme is called hydrostatic relaxation scheme which is a robust and straightforward scheme. This scheme is given as the hydrostatic reconstruction of the relaxation solver. Some numerical tests are presented such as analytical solution, transcritical flow over a granular bump, and erodible bottom due to dam-break. The comparisons of numerical and data experiments are also given in dam-break over granular bed simulation. The results of our simulation have a good agreement with analytical solution and the data experiments. Moreover, satisfactory convergence rate in L1-norm is obtained.
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