A Stable and Efficient Flood Routing Model Based on Unstructured Grid

2020 ◽  
Author(s):  
Shan Zhou ◽  
Hongchang Hu
Keyword(s):  
Shallow Water ◽  
Computational Cost ◽  
Flood Routing ◽  
Test Cases ◽  
Reconstruction Method ◽  
Two Dimensional ◽  
Time Stepping ◽  
Shallow Water Flows ◽  
Local Time Stepping ◽  
Muscl Reconstruction

<p>Godunov-type schemes are widely applied to solve shallow water equations. In this study, a novel non-negative water depth Multislope MUSCL reconstruction method is incorporated into a two-dimensional unstructured cell-centered Godunov-type finite volume model to simulate shallow water flows, It is verified that the method performs well in avoiding non-physical oscillation and also has well-balanced performance by simulate three test cases. Due to the limitation of CFL conditions, mesh refinement will greatly increase the computational cost. In this study, A Local Time Stepping(LTS) strategy is specifically designed to greatly improve the computational efficiency. In addition, in order to make the model suitable for more application scenarios, we have realized the coupling of one-dimensional and two-dimensional models. Based on the above three improvements, we have developed a stable and efficient flood routing model.</p>

scholarly journals A New Well-Balanced Reconstruction Technique for the Numerical Simulation of Shallow Water Flows with Wet/Dry Fronts and Complex Topography

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1661 ◽  
Author(s):  
Zhengtao Zhu ◽  
Zhonghua Yang ◽  
Fengpeng Bai ◽  
Ruidong An
Keyword(s):  
Shallow Water ◽  
Water System ◽  
Reconstruction Technique ◽  
Test Cases ◽  
Bed Topography ◽  
Surface Gradient ◽  
Shallow Water Flows ◽  
Shallow Water System ◽  
The One ◽  
Flow Variables

This study develops a new well-balanced scheme for the one-dimensional shallow water system over irregular bed topographies with wet/dry fronts, in a Godunov-type finite volume framework. A new reconstruction technique that includes flooded cells and partially flooded cells and preserves the non-negative values of water depth is proposed. For the wet cell, a modified revised surface gradient method is presented assuming that the bed topography is irregular in the cell. For the case that the cell is partially flooded, this paper proposes a special reconstruction of flow variables that assumes that the bottom function is linear in the cell. The Harten–Lax–van Leer approximate Riemann solver is applied to evaluate the flux at cell faces. The numerical results show good agreement with analytical solutions to a set of test cases and experimental results.

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.

A local time stepping algorithm for GPU-accelerated 2D shallow water models

2018 ◽  
Vol 111 ◽  
pp. 274-288 ◽  
Author(s):  
Susanna Dazzi ◽  
Renato Vacondio ◽  
Alessandro Dal Palù ◽  
Paolo Mignosa
Keyword(s):  
Shallow Water ◽  
Local Time ◽  
Time Stepping ◽  
Local Time Stepping ◽  
Shallow Water Models ◽  
Water Models

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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