A well-balanced numerical model for depth-averaged two-layer shallow water flows

2021 ◽  
Vol 40 (8) ◽  
Author(s):  
Xin Liu ◽  
Junfeng He
2014 ◽  
Vol 580-583 ◽  
pp. 1793-1798
Author(s):  
Biao Lv ◽  
Shao Xi Li

Based on well-balanced Roe’s approximate Riemann solver, a numerical model is developed for the unsteady, two-dimensional, shallow water flow with variable topographies. In this model, an efficient methods are applied to treat the source terms and to satisfy the compatibility condition on unstructured grids. In the method, different components of the bed slope source term are considered separately and the compatible discretization of the components is presented. The newly developed model is verified against analytical solutions and measured date, with good agreement.


2017 ◽  
Vol 154 ◽  
pp. 1-11
Author(s):  
Xin Liu ◽  
Abdolmajid Mohammadian ◽  
Julio Ángel Infante Sedano

2012 ◽  
Vol 138 (2) ◽  
pp. 122-132 ◽  
Author(s):  
Yongcan Chen ◽  
Zhiyong Wang ◽  
Zhaowei Liu ◽  
Dejun Zhu

2019 ◽  
Vol 37 (2) ◽  
pp. 401-429 ◽  
Author(s):  
Thomas Rowan ◽  
Mohammed Seaid

Purpose The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the single-layered models have been used to model shallow water flows over erodible beds. Although such models present a real opportunity for shallow water flows over movable beds, this paper is the first to propose a multilayered solver for this class of flow problems. Design/methodology/approach Multilayered beds formed with different erodible soils are considered in this study. The governing equations consist of the well-established shallow water equations for the flow, a transport equation for the suspended sediments, an Exner-type equation for the bed load and a set of empirical equations for erosion and deposition terms. For the numerical solution of the coupled system, the authors consider a non-homogeneous Riemann solver equipped with interface-tracking tools to resolve discontinuous soil properties in the multilayered bed. The solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. Findings This paper reveals that modeling shallow water flows over multilayered sedimentary topography can be achieved by using a coupled system of partial differential equations governing sediment transport. The obtained results demonstrate that the proposed numerical model preserves the conservation property, and it provides accurate results, avoiding numerical oscillations and numerical dissipation in the approximated solutions. Originality/value A novel implementation of sediment handling is presented where both averaged and separate values for sediment species are used to ensure speed and precision in the simulations.


Sign in / Sign up

Export Citation Format

Share Document