The Numerical Modeling Method Of Dividing-Wave Based On Boussinesq Equation

In the coast engineering and offing-shoal design ,the wave element is one of themain ingredients .In the fact engineering ,it is very important to exactly model thewave. In this paper, we firstly review the Boussinesq equation wave model'sdevelopment in this decades of years, and then advance a new wave numericalmodel based on Boussinesq equation. The main idea is: First, we divide the verticalvelocity profile into several layers, then integral to the velocity profile in every layer,evaluate the average velocity in the every layer, and use this average velocity toreplace every layer velocity, add up to the interface boundary conditions of each layerto resolve the velocity, free-face. Here, we emphasize to discuss the One-layer andTwo-layer models, the One-Layer model is the Boussinesq equation as we hadknown .Using the One-layer model ,there is a good linear dispersion when kh≈3, inthe middle-depth, the relative error of nonlinear is very larger than linear. Afternonlinear improving, the nonlinear accuracy arrives at the kh ≈3.The Two-layermodel has accurate linear character when kh ≈8,and accurate nonlinear characterwhen kh≈6.The numerical method is the predictor-correct means of finite differenceprinciple, in the predictor phase ,using the third-order Adams-Bashforth explicitformat, in the correct phase ,using the fourth-order Adams-Moulton implicit format.In the same time ,adds up to the bottom friction and wave breaking in the momentumequation . The moving boundary applies the linear extrapolation method. The aroundboundaries apply absorb boundaries and solid wall boundaries. Absorb boundary usesponge-absorb layer, applying some wave lengths sponge-absorb layer ,we canacquire good effects to wave absorb.In this paper ,the one-dimension simulation ,we use the regular wave propagationover submerged bar ,comparing the two-layer result and the one-layer result and theexperiment result ,we can see the two-layer can accurately model the second and thirdharmonious, and the accuracy is increasing. In additional , we model the solitary waveclimbing the slope ,emerging the allover course of the solitary wave from climbing tobreaking. As we known , compare others wave models , the largest excellence ofthe Boussinesq equation wave model is solving two-dimension problems. So weemphasize on the two-dimension problems. Here, we model the regular wavepropagation over the submerged ellipse shoal , compare to the experiment result , wecan see it is very accuracy to model two-dimension wave problems. Another, we usethe example of wave over deep waterway propagation , applying numerical model ,wecan see the waterway significantly affects the wave propagation after the waterwaydigging, it is very instructive to direct our fact engineering.