scholarly journals Iber applications basic guide. Two-dimensional modelling of free surface shallow water flows

2019 ◽  
Author(s):  
Luis Cea Gómez ◽  
Ernest Bladé i Castellet ◽  
Marcos Sanz Ramos ◽  
María Bermúdez Pita ◽  
Ángel Mateos Alonso
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Two Dimensional ◽  
Water Flows ◽  
Shallow Water Flows

A Two-Dimensional Numerical Model for Shallow Water Flows over Variable Topographies

2014 ◽  
Vol 580-583 ◽  
pp. 1793-1798
Author(s):  
Biao Lv ◽  
Shao Xi Li
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Source Term ◽  
Unstructured Grids ◽  
Riemann Solver ◽  
Two Dimensional ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Bed Slope ◽  
Good Agreement

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.

scholarly journals Weak Local Residuals as Smoothness Indicators in Adaptive Mesh Methods for Shallow Water Flows

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 345
Author(s):  
Sudi Mungkasi ◽  
Stephen Gwyn Roberts
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Numerical Solutions ◽  
Adaptive Mesh ◽  
Finite Volume Methods ◽  
Water Type ◽  
Two Dimensional ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Smoothness Indicators

This paper proposes some formulations of weak local residuals of shallow-water-type equations, namely, one-, one-and-a-half-, and two-dimensional shallow water equations. Smooth parts of numerical solutions have small absolute values of weak local residuals. Rougher parts of numerical solutions have larger absolute values of weak local residuals. This behaviour enables the weak local residuals to detect parts of numerical solutions which are smooth and rough (non-smooth). Weak local residuals that we formulate are implemented successfully as refinement or coarsening indicators for adaptive mesh finite volume methods used to solve shallow water equations.

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