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The Physics of Fluids
Variable-coefficient equations can be used to describe certain phenomena when inhomogeneous media and nonuniform boundaries are taken into consideration.
Xing Lü, Liang-Li Zhang, Wen-Xiu Ma
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Variable-coefficient equations can be used to describe certain phenomena when inhomogeneous media and nonuniform boundaries are taken into consideration.
Xing Lü, Liang-Li Zhang, Wen-Xiu Ma
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Ocean Engineering, 2018
In this article, we establish the exact wave solutions of the Boussinesq equation and the (2 + 1)-dimensional extended shallow water wave equation by applying the new generalized ( G ' / G ) -expansion method. When the condition of the fluid is such that
Md. Dulal Hossain +2 more
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In this article, we establish the exact wave solutions of the Boussinesq equation and the (2 + 1)-dimensional extended shallow water wave equation by applying the new generalized ( G ' / G ) -expansion method. When the condition of the fluid is such that
Md. Dulal Hossain +2 more
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On the Shallow Water Equations
Zeitschrift für Naturforschung A, 2017AbstractWe studied the shallow water equations of nonlinear conservation laws. First we studied the parametrisation of nonlinear elementary waves and hence we present the solution to the Riemann problem. We also prove the uniqueness of the Riemann solution. The Riemann invariants are formulated.
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Symmetric truncations of the shallow-water equations
Physical Review E, 1993Conservation of potential vorticity in Eulerian fluids reflects [ital particle] [ital interchange] [ital symmetry] in the Lagrangian fluid version of the same theory. The algebra associated with this symmetry in the shallow-water equations is studied here, and we give a method for truncating the degrees of freedom of the theory which preserves a ...
, Rouhi, , Abarbanel
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Dispersive Nonlinear Shallow‐Water Equations
Studies in Applied Mathematics, 2009A set of dispersive and hyperbolic depth‐averaged equations is obtained using a hyperbolic approximation of a chosen set of fully nonlinear and weakly dispersive Boussinesq‐type equations. These equations provide, at a reasonably reduced cost, both a physically sound description of the nearshore dynamics and a complete representation of dispersive and ...
Antuono, M. +2 more
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An implicit wave equation model for the shallow water equations
Advances in Water Resources, 1984In this paper an implicit numerical solution procedure for the shallow water equations is presented. It achieves efficiency through replacement of decompositions of a time-varying matrix by back substitutions for the solution of the equation system.
Ingemar P. E. Kinnmark, William G. Gray
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On ?The shallow water equations? By M. Shinbrot
Journal of Engineering Mathematics, 1972The paper [1] above describes two steady shallow water flows which differ from the known flows of this type. It is suggested that the conditions imposed in obtaining these solutions are not consistent.
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Normalized shallow water equations
Moscow University Physics Bulletin, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elizarova, T. G., Afanasieva, M. V.
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Analytic solutions to the shallow water equations
Physical Review E, 2005Analytic, two-dimensional steady-state solutions to the rotating shallow water equations over variable topography are derived, by exploiting a drastic simplification of the equilibrium problem that occurs for nondivergent flows. For such flows, the equilibrium system decouples, and the cross-stream component of the momentum equation formally reduces to
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