# Visualization Study of fKdV Equation Simulation with Matlab

Conference Paper · January 2008with10 Reads
DOI: 10.1109/ISCSCT.2008.92 · Source: DBLP
Conference: 2008 International Symposium on Computer Science and Computational Technology, ISCSCT 2008, 20-22 December 2008, Shanghai, China, 2 Volumes
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.
• ##### Effects of varying bottom on nonlinear surface waves
[Show abstract] [Hide abstract] 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.
Article · Mar 2006
• ##### The Fission and Disintegration of Internal Solitary Waves Moving over Two-Dimensional Topography
[Show abstract] [Hide abstract] ABSTRACT: The propagation of long internal waves over two-dimensional topography is discussed. A two-dimensional version of the Korteweg-deVries equation is derived with variable coefficients which depend on the local fluid depth. The fission law for solitary waves propagating into shallower water for two density stratification models and the possible disintegration of a solitary wave into a dispersive packet are discussed on the basis of this equation. (A)
Article · Oct 1978
• ##### Subcritical, transcritical and supercritical flows over a step
[Show abstract] [Hide abstract] ABSTRACT: Free-surface flow over a bottom topography with an asymptotic depth change (a `step') is considered for dierent ranges of Froude numbers varying from subcritical, transcritical, to supercritical. For the subcritical case, a linear model indicates that a train of transient waves propagates upstream and eventually alters the conditions there. This leading-order upstream influence is shown to have profound eects on higher-order perturbation models as well as on the Froude number which has been conventionally dened in terms of the steady-state upstream depth. For the transcritical case, a forced Korteweg{de Vries (fKdV) equation is derived, and the numerical solution of this equation reveals a surprisingly conspicuous distinction between positive and negative forcings. It is shown that for a negative forcing, there exists a physically realistic nonlinear steady state and our preliminary results indicate that this steady state is very likely to be stable. Clearly in contrast to previous ndings associated with other types of forcings, such a steady state in the transcritical regime has never been reported before. For transcritical flows with Froude number less than one, the upstream influence discovered for the subcritical case reappears.
Full-text · Article · Feb 1997