Exact solution for a density contrast shallow‐water wedge using normal coordinates

1990 ◽  
Vol 87 (6) ◽  
pp. 2442-2450 ◽  
Author(s):  
Dezhang Chu
Keyword(s):  
Exact Solution ◽  
Shallow Water ◽  
Density Contrast ◽  
Normal Coordinates

New exact solutions for the Wick-type stochastic Zakharov–Kuznetsov equation for modelling waves on shallow water surfaces

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
S. Saha Ray ◽  
S. Singh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Exact Solutions ◽  
White Noise ◽  
Shallow Water ◽  
Hermite Transform ◽  
New Exact Solutions ◽  
Kudryashov Method ◽  
Stochastic Solution

AbstractIn this article, an exact solution of the Wick-type stochastic Zakharov–Kuznetsov equation has been obtained by using the Kudryashov method. We have used the Hermite transform for transforming the Wick-type stochastic Zakharov–Kuznetsov equation into a deterministic partial differential equation. Also we have applied the inverse Hermite transform for obtaining a set of stochastic solution in the white noise space.

scholarly journals Run-up of nonlinear monochromatic wave on a plane beach in presence of a tide

2019 ◽  
Vol 59 (4) ◽  
pp. 529-532
Author(s):  
I. I. Didenkulova ◽  
E. N. Pelinovsky
Keyword(s):  
Exact Solution ◽  
Shallow Water ◽  
Nonlinear Problem ◽  
Incident Wave ◽  
Wave Amplitude ◽  
Monochromatic Wave ◽  
Shallow Water Theory ◽  
Long Wave ◽  
Run Up

The nonlinear problem of long wave run-up on a plane beach in a presence of a tide is solved within the shallow water theory using the Carrier-Greenspan approach. The exact solution of the nonlinear problem for wave run-up height is found as a function of the incident wave amplitude. Influence of tide on characteristics of wave run-up on a beach is studied.

Elastic and Annihilation Solitons of the (3+1)-Dimensional Generalized Shallow WaterWave System

2013 ◽  
Vol 68 (5) ◽  
pp. 350-354 ◽  
Author(s):  
Song-Hua Ma ◽  
Jian-Ping Fang ◽  
Hong-Yu Wu
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Wave Solution ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Separation Method ◽  
Variable Separation ◽  
Variable Separation Method

With the help of the symbolic computation system Maple, the mapping approach, and a linear variable separation method, a new exact solution of the (3+1)-dimensional generalized shallow water wave (GSWW) system is derived. Based on the obtained solitary wave solution, some novel soliton excitations are investigated.

Two kinds of multi-order exact solution to the shallow water system

2010 ◽  
Vol 81 (2) ◽  
pp. 025011 ◽  
Author(s):  
Zuntao Fu ◽  
Linna Zhang ◽  
Jiangyu Mao ◽  
Shikuo Liu
Keyword(s):  
Exact Solution ◽  
Shallow Water ◽  
Water System ◽  
Shallow Water System

scholarly journals Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 364-370 ◽  
Author(s):  
Dumitru Baleanu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Aliyu Isa Aliyu
Keyword(s):  
Exact Solution ◽  
Wave Equation ◽  
Conservation Laws ◽  
Shallow Water ◽  
Water Wave ◽  
Airy Function ◽  
One Dimensional ◽  
Shallow Water Wave ◽  
Differential Substitution ◽  
Conservation Theorem

AbstractIn this article, the generalized shallow water wave (GSWW) equation is studied from the perspective of one dimensional optimal systems and their conservation laws (Cls). Some reduction and a new exact solution are obtained from known solutions to one dimensional optimal systems. Some of the solutions obtained involve expressions with Bessel function and Airy function [1,2,3]. The GSWW is a nonlinear self-adjoint (NSA) with the suitable differential substitution, Cls are constructed using the new conservation theorem.

scholarly journals Advanced Numerical Solver for Dam-Break Flow Application

2011 ◽  
Vol 14 (1) ◽  
pp. 73
Author(s):  
Jaan Hui Pu ◽  
Zhumabay Bakenov ◽  
Desmond Adair
Keyword(s):  
Exact Solution ◽  
Shallow Water ◽  
Rectangular Channel ◽  
Dam Break ◽  
Test Case ◽  
Upwind Schemes ◽  
Dam Break Flow ◽  
Slope Limiters ◽  
Bed Slope ◽  
Numerical Solver

In this paper, a HLL (Harten Lax van Leer) approximate Riemann solver with MUSCL scheme (Monotonic Upwind Schemes for Conservative Laws) is implemented in the presented FV (Finite Volume) model. The presented model is used to simulate different dam-break flow events to verify its capability. Four test cases are presented in this paper. In the first test case, a 1-Dimensional (1D) dambreak flow is simulated over a rectangular channel with different slope limiters of the FV model (namely Godunov, Superbee, Minmod, van Leer, and van Albada). The second test case consists of a simulation of shallow water discontinuous dam-break flow over a dry-downstream bed channel. The third test simulates the shallow water dam-break flow with the existence of bed slope and bed shear stress. Finally, in the last test, the HLL-MUSCL model used in this paper and some other solver models used in literature are compared against the referred exact solution in dam-break flow application. The presented HLL-MUSCL scheme is found to give the best agreement to the exact solution.

Sign in / Sign up

Export Citation Format

Share Document