@Article{IJNAM-18-2,
author = {Xian, Weizhi and Chen, Aimin and Yongping, Cheng and Haiyun, Dong},
title = {Numerical Simulations for Shallow Water Flows over Erodible Beds by Central DG Methods},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2021},
volume = {18},
number = {2},
pages = {143--164},
abstract = {<p style="text-align: justify;">In this paper, we investigate the shallow water flows over erodible beds by using a
fully coupled mathematical model in two-dimensional space. This model combines the nonlinear
shallow water equations, the sediment transport equation and the bed evolution equation. The
purpose of this paper is to design a well-balanced and positivity-preserving scheme for this model.
In order to achieve the well-balanced property, the coupled system is first reformulated as a new
form by introducing an auxiliary variable. The central discontinuous Galerkin method is applied
to discretize the model. By choosing the value of the auxiliary variable suitably, the scheme can
exactly balance the flux gradients and source terms in the &quot;still-water&quot; case, and thus the well-balanced property of the proposed scheme can be proved. Moreover, the non-negativity of the
volumetric sediment concentration in the sediment transport equation is maintained by choosing
a suitable time step and using a positivity-preserving limiter. Numerical tests are presented to
illustrate the validity of the proposed scheme.<br/></p>},
issn = {2617-8710},
doi = {https://doi.org/2021-IJNAM-18712},
url = {https://global-sci.com/article/82976/numerical-simulations-for-shallow-water-flows-over-erodible-beds-by-central-dg-methods}
}