scholarly journals A two-dimensional artificial viscosity technique for modelling discontinuity in shallow water flows

2017 ◽  
Vol 45 ◽  
pp. 653-683 ◽  
Author(s):  
Bobby Minola Ginting
Keyword(s):  
Shallow Water ◽  
Artificial Viscosity ◽  
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.

scholarly journals A Discontinuous Galerkin Method for Two-Dimensional Shock Wave Modeling

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
W. Lai ◽  
A. A. Khan
Keyword(s):  
Shock Waves ◽  
Galerkin Method ◽  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Dam Break ◽  
Two Dimensional ◽  
Simple Method ◽  
Water Flows ◽  
Shallow Water Flows

A numerical scheme based on discontinuous Galerkin method is proposed for the two-dimensional shallow water flows. The scheme is applied to model flows with shock waves. The form of shallow water equations that can eliminate numerical imbalance between flux term and source term and simplify computation is adopted here. The HLL approximate Riemann solver is employed to calculate the mass and momentum flux. A slope limiting procedure that is suitable for incompressible two-dimensional flows is presented. A simple method is adapted for flow over initially dry bed. A new formulation is introduced for modeling the net pressure force and gravity terms in discontinuous Galerkin method. To validate the scheme, numerical tests are performed to model steady and unsteady shock waves. Applications include circular dam break with shock, shock waves in channel contraction, and dam break in channel with bend. Numerical results show that the scheme is accurate and efficient to model two-dimensional shallow water flows with shock waves.

SIGNIFICANCE OF AVERAGING COEFFICIENTS IN STABILITY ANALYSIS OF SHALLOW WAKE FLOWS

2007 ◽  
Vol 12 (3) ◽  
pp. 357-368
Author(s):  
Andrei Kolyshkin
Keyword(s):  
Stability Analysis ◽  
Shallow Water ◽  
Nonlinear Stability ◽  
Water Depth ◽  
Coherent Structures ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Wake Flows ◽  
Water Flows ◽  
Shallow Water Flows

Flows behind obstacles (such as islands) are shallow if the transverse scale of the flow is much larger than water depth. Field, laboratory and numerical data show that the flow pattern in shallow wakes exhibits a complex eddy‐like motion. Experimental and theoretical analyses provide evidence for the presence of two‐dimensional coherent structures in shallow water flows and show that the development of shallow wakes is different from the wakes in deep water due to the following reasons: first, the development of three‐dimensional instabilities is prevented by limited water depth and second, bottom friction acts as a stabilizing mechanism for suppressing the transverse growth of perturbations. Several authors have used the linear and weakly nonlinear stability theory in order to understand when shallow flows become unstable. Two‐dimensional depth‐averaged Saint‐Venant equations are usually used for the analysis. One of the main assumptions in shallow water theory is the independence of the velocity distribution on the vertical coordinate. In many cases, however, this assumption may not be valid. This paper presents an attempt to evaluate the influence of the assumption on the results of linear stability analysis of shallow wake flows with bottom friction. Momentum correction coefficients β 1 and β 2 are used in order to take into account the non‐uniformity of the velocity distribution in the vertical direction. Linear stability calculations show that the stability boundary is quite sensitive to the variation of the parameters β 1 and β 2. The role of the linear and weakly nonlinear stability analysis on the formation of two‐dimensional coherent structures in shallow water flows is discussed.

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
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