scholarly journals An Unstructured Finite-Volume Technique for Shallow-Water Flows With Wetting and Drying Fronts

2011 ◽  
Author(s):  
Kim Dan Nguyen ◽  
Rajendra K. Ray
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Present Model ◽  
Numerical Solutions ◽  
Mass Conservation ◽  
Least Square ◽  
Wetting And Drying ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Drying Treatment

An unstructured finite volume numerical model is presented here for simulating shallow-water flows with wetting and drying fronts. The model is based on the Green’s theorem in combination with Chorin’s projection method. A 2nd-order upwind scheme coupled with a Least Square technique is used to handle convection terms. An Wetting and drying treatment is used in the present model to ensures the total mass conservation. To test it’s capacity and reliability, the present model is used to solve the Parabolic Bowl problem. We compare our numerical solutions with the corresponding analytical and existing standard numerical results. Excellent agreements are found in all the cases.

A Weil-Balanced Node-Centered Finite Volume Scheme for Shallow Water Flows with Wetting and Drying

2009 ◽  
Author(s):  
A. I. Delis ◽  
I. K. Nikolos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Finite Volume Scheme ◽  
Wetting And Drying ◽  
Volume Scheme ◽  
Water Flows ◽  
Shallow Water Flows

Quasi-two-layer finite-volume scheme for modelling shallow water flows over an arbitrary bed in the presence of external force. II. Algorithm applications and numerical results

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Kirill V. Karelsky ◽  
Arakel S. Petrosyan ◽  
Alexander G. Slavin
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
External Force ◽  
Large Scale ◽  
Lower Layer ◽  
Three Dimensional ◽  
Finite Volume Scheme ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Scale Motion

AbstractA finite-volume numerical method for studying shallow water flows over an arbitrary bed profile in the presence of external force has been proposed in [33]. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with advanced consideration of the flow features near the step. A distinctive feature of the suggested model is a separation of the studied flow into two layers in calculating the flow quantities near each step, and improving by this means the approximation of depth-averaged solutions of the initial three-dimensional Euler equations. We are solving the shallow-water equations for one layer, introducing the fictitious lower layer only as an auxiliary structure in setting up the appropriate Riemann problems for the upper layer. Besides, the quasi-two-layer approach leads to the appearance of additional terms in the one-layer finite-difference representation of balance equations. Numerical simulations are performed based on the proposed in [33] algorithm of various physical phenomena, such as breakdown of the rectangular fluid column over an inclined plane, large-scale motion of fluid in the gravity field in the presence of Coriolis force over amounted obstacle on the underlying surface. Computations are made for the two-dimensional dam-break problem on a slope precisely conform to laboratory experiments. The interaction of the Tsunami wave with the shore line including an obstacle has been simulated to demonstrate the efficiency of the developed algorithm in domains, including partly flooded and dry regions.

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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