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- Title
NUMERICAL SIMULATIONS FOR SHALLOW WATER FLOWS OVER ERODIBLE BEDS BY CENTRAL DG METHODS.
- Authors
WEIZHI XIAN; AIMIN CHEN; YONGPING CHENG; HAIYUN DONG
- Abstract
In this paper, we investigate the shallow water fllows 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 rst 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 "still-water" case, and thus the wellbalanced 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.
- Subjects
WATER depth; SHALLOW-water equations; TRANSPORT equation; EVOLUTION equations; SEDIMENT transport
- Publication
International Journal of Numerical Analysis & Modeling, 2021, Vol 18, Issue 2, p143
- ISSN
1705-5105
- Publication type
Article