Conference Paper

Visualization Study of fKdV Equation Simulation with Matlab.

DOI: 10.1109/ISCSCT.2008.92 Conference: 2008 International Symposium on Computer Science and Computational Technology, ISCSCT 2008, 20-22 December 2008, Shanghai, China, 2 Volumes
Source: DBLP

ABSTRACT Numerical simulation results of fKdV equation are illustrated in the forms of waterfall with Matlab. Matlab can solve many complicated engineering problem and the numerical results can be showed by its excellent graphics. The forced Kortewege-de Vries (fKdV) equation was regarded as a classical nonlinear model when the resonant flow was happened. Which involves a balance between non-linearity and dispersion at leading-order and the effect of the bottom. The pseudo-spectral method based on function approach was good for solving nonlinear equation, and it is convenience to program with the Matlab for PS method. With the results, we can get some conclusion about the effect of the different bottom on surface wave.

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    ABSTRACT: The resonant flow of an incompressible, inviscid fluid with surface tension on varying bottoms was researched. The effects of different bottoms on the nonlinear surface waves were analyzed. The waterfall plots of the wave were drawn with Matlab according to the numerical simulation of the fKdV equation with the pseudo-spectral method. From the waterfall plots, the results are obtained as follows: for the convex bottom, the waves system can be viewed as a combination of the effects of forward-step forcing and backwardstep forcing, and these two wave systems respectively radiate upstream and downstream without mutual interaction. Nevertheless, the result for the concave bottom is contrary to the convex one. For some combined bottoms, the wave systems can be considered as the combination of positive forcing and negative forcing.
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