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June 2006 A Finite Element Scheme for Two-Layer Viscous Shallow-Water Equations
Hiroshi Kanayama, Hiroshi Dan
Japan J. Indust. Appl. Math. 23(2): 163-191 (June 2006).


In this paper, the two-layer viscous shallow-water equations are derived from the threedimensional Navier-Stokes equations under the hydrostatic assumption. It is noted that the combination of upper and lower equations in the two-layer model produces the classical one-layer equations if the density of each layer is the same. The two-layer equations are approximated by a finite element method which follows our numerical scheme established for the one-layer model in 1978. Finally, it is numerically demonstrated that the interfacial instability generated when the densities are the same can be eliminated by providing a sufficient density difference.


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Hiroshi Kanayama. Hiroshi Dan. "A Finite Element Scheme for Two-Layer Viscous Shallow-Water Equations." Japan J. Indust. Appl. Math. 23 (2) 163 - 191, June 2006.


Published: June 2006
First available in Project Euclid: 12 September 2006

MathSciNet: MR2245699
zbMATH: 1149.76638

Keywords: finite element scheme , layer model , Navier-Stokes equations , shallow-water

Rights: Copyright © 2006 The Japan Society for Industrial and Applied Mathematics

Vol.23 • No. 2 • June 2006
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