Projection finite volume method for shallow water flows

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

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Discussion of “Finite Volume Model for Two-Dimensional Shallow Water Flows on Unstructured Grids” by Tae Hoon Yoon and Seok-Koo Kang

Journal of Hydraulic Engineering ◽

10.1061/(asce)0733-9429(2005)131:12(1147.2) ◽

2005 ◽

Vol 131 (12) ◽

pp. 1147-1148 ◽

Cited By ~ 2

Author(s):

Davood Farshi ◽

Siamak Komaei

Keyword(s):

Shallow Water ◽

Finite Volume ◽

Unstructured Grids ◽

Two Dimensional ◽

Water Flows ◽

Finite Volume Model ◽

Volume Model ◽

Shallow Water Flows

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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

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2014-0014 ◽

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.

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