scholarly journals Comparison of Numerical Methods for SWW Equations

2019 ◽  
Vol 7 (09) ◽  
Author(s):  
Shkelqim Hajrulla ◽  
Leonard Bezati ◽  
Besiana Hamzallari
Keyword(s):  
Wave Equation ◽  
Numerical Methods ◽  
Finite Volume Method ◽  
Water Wave ◽  
Decomposition Method ◽  
Wave Equations ◽  
Kdv Equation ◽  
The Third ◽  
Laplace Decomposition Method ◽  
Volume Method

Abstract: In this paper we consider three methods of approximation for the nonlinear water wave equation. In particular we are interested of KdV equation as a stationary water wave. The first is the method of approximation with a polynomial, the second method is the finite–volume method and the third method is Laplace decomposition method (LDM). A comparison between the methods is mentioned in this article. We treat the considered methods comparing the obtained solutions with the exact ones. We give in particular the numerical results compared with the analytical results. We show that the used methods are effective and convenient for solving the water wave equations. We can propose and sure that the method of approximation with a polynomial gives accurate results.

scholarly journals Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equation in Fractal Strings

2019 ◽  
Vol 3 (2) ◽  
pp. 26 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Kamil Jassim
Keyword(s):  
Wave Equation ◽  
Decomposition Method ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Damped Wave Equation ◽  
Fractal Strings ◽  
Fractional Derivative Operators ◽  
Laplace Decomposition Method ◽  
Dissipative Wave Equation

In this paper, we apply the local fractional Laplace variational iteration method (LFLVIM) and the local fractional Laplace decomposition method (LFLDM) to obtain approximate solutions for solving the damped wave equation and dissipative wave equation within local fractional derivative operators (LFDOs). The efficiency of the considered methods are illustrated by some examples. The results obtained by LFLVIM and LFLDM are compared with the results obtained by LFVIM. The results reveal that the suggested algorithms are very effective and simple, and can be applied for linear and nonlinear problems in sciences and engineering.

A Hybrid Unstructured/Spectral Method for the Resolution of Navier-Stokes Equations

2009 ◽  
Author(s):  
Roque Corral ◽  
Javier Crespo
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
High Order ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
The Third ◽  
Third Dimension ◽  
Volume Method

A novel high-order finite volume method for the resolution of the Navier-Stokes equations is presented. The approach combines a third order finite volume method in an unstructured two-dimensional grid, with a spectral approximation in the third dimension. The method is suitable for the resolution of complex two-dimensional geometries that require the third dimension to capture three-dimensional non-linear unsteady effects, such as those for instance present in linear cascades with separated bubbles. Its main advantage is the reduction in the computational cost, for a given accuracy, with respect standard finite volume methods due to the inexpensive high-order discretization that may be obtained in the third direction using fast Fourier transforms. The method has been applied to the resolution of transitional bubbles in flat plates with adverse pressure gradients and realistic two-dimensional airfoils.

Viscoelastic time-reversal imaging

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. A45-A50 ◽  
Author(s):  
Tieyuan Zhu
Keyword(s):  
Wave Equation ◽  
Time Reversal ◽  
Wave Equations ◽  
Homogeneous Model ◽  
S Wave ◽  
The Third ◽  
Complex Source ◽  
Imaging Approach ◽  
Time Invariance ◽  
Time Invariant

The time invariance of wave equations, an essential precondition for time-reversal (TR) imaging, is no longer valid when introducing attenuation. I evaluated a viscoelastic (VE) TR imaging algorithm based on a novel VE wave equation. By reversing the sign of the P- and S-wave loss operators, the VE wave equation became time invariant for the TR operation. Attenuation effects were thus compensated for during TR wave propagation. I developed the formulations of VE forward modeling and TR imaging. I tested my imaging approach in three numerical experiments. The first experiment used a 2D homogeneous model with full-aperture receivers to examine the time invariance of the VE TR imaging equation. Using the same model, the second experiment was used to demonstrate the method’s ability to characterize a point source. In the third experiment, I applied this method to characterize a complex source using borehole geophones. Numerical results illustrated that the VE TR imaging improved our knowledge of the source location, radiation pattern, and amplitude.

Particular Solutions for a (3+1)-dimensional Generalized Shallow Water Wave Equation

1998 ◽  
Vol 53 (9) ◽  
pp. 806-807 ◽  
Author(s):  
Yi-Tian Gao ◽  
Bo Tian ◽  
Woopyo Hong
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Wave Equations ◽  
Current Interest ◽  
Particular Solutions ◽  
Shallow Water Wave ◽  
New Family ◽  
Shallow Water Wave Equations

Abstract The shallow water wave equations (SWWEs) are of current interest in nonlinear sciences. In this paper we obtain a new family of soliton-like solutions for a (3-1)-dimensional generalized SWWE. Samples are given.

Solitons and integrability for a (2+1)-dimensional generalized variable-coefficient shallow water wave equation

2017 ◽  
Vol 31 (03) ◽  
pp. 1750012 ◽  
Author(s):  
Ya-Le Wang ◽  
Yi-Tian Gao ◽  
Shu-Liang Jia ◽  
Zhong-Zhou Lan ◽  
Gao-Fu Deng ◽  
...  
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Bell Polynomials ◽  
Shallow Water Wave ◽  
Binary Bell Polynomials

Under investigation in this paper is a (2[Formula: see text]+[Formula: see text]1)-dimensional generalized variable-coefficient shallow water wave equation which can be reduced to several integrable equations, such as the Korteweg–de Vries (KdV) equation and the Calogero–Bogoyavlenskii–Schiff (CBS) equation. Bilinear forms, Bäcklund transformation, Lax pair and infinite conservation laws are derived based on the binary Bell polynomials. N-soliton solutions are constructed via the Hirota method. Propagation and interaction of the solitons are illustrated graphically: (i) variable coefficients affect the shape of the N-soliton interaction in the scaled space and time coordinates; (ii) positions of the solitons depend on the sign of wave numbers after each interaction; (iii) interaction of the solitons is elastic, i.e. the amplitude, velocity and shape of each soliton remain invariant after each interaction except for a phase shift.

scholarly journals Analytic solution of the linearized shallow-water wave equations for certain continuous depth variations

1975 ◽  
Vol 19 (1) ◽  
pp. 81-94 ◽  
Author(s):  
D. L. Clements ◽  
C. Rogers
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Ground Motion ◽  
Water Depth ◽  
Water Wave ◽  
Wave Equations ◽  
Analytic Solution ◽  
Governing Equations ◽  
Long Wave ◽  
Shallow Water Wave Equations

AbstractThe linear long-wave equations with (and without) small ground motion are considered. The governing equations are represented in a matrix from and transformations are sought which reduce the system to (for example) a form associated with the conventional wave equation. Integration of the system is then immediate. It is shown that such a reduction may be acheived provided the variation in water depth is specified by certain multi-parameter forms.

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