Geodesic
Numerical modelling of the fluid flow above the bottom topography
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2014), pp. 51-60

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This paper presents an investigation of an inviscid incompressible fluid flow in a straight section of a channel with an irregular bottom as a closure of river stream model. Mathematically, the problem is written as a boundary-value problem for shallow water equations. Three test computational examples for a steady and unsteady flow above regular and irregular bottom have been carried out to study the model and possibilities of its applications. The computed solutions are obtained using the finite-difference method with the first order UPWIND scheme and two-step Lax–Wendroff scheme, which is second-order accurate in both space and time. To suppress dispersion characteristics which are the feature of second-order schemes, Kolgan’s surfacing algorithm is used. Numerical solutions obtained by the aforesaid schemes well agree with each other and become equivalent upon mesh clustering. In addition, a model of the contaminant dispersion in a stream over an irregular bottom is constructed. The computed distribution of the contaminant is in a good agreement with the physical flow pattern.
Keywords: mathematical model, shallow water equations, approximation error, solution stability, solution smoothing. 
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     author = {V. V. Churuksaeva and M. D. Mikhailov},
     title = {Numerical modelling of the fluid flow above the bottom topography},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {51--60},
     publisher = {mathdoc},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/VTGU_2014_1_a4/}
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V. V. Churuksaeva; M. D. Mikhailov. Numerical modelling of the fluid flow above the bottom topography. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2014), pp. 51-60. http://geodesic.mathdoc.fr/item/VTGU_2014_1_a4/