# NONLINEAR WAVE COLLISION AGAINST FULLY AND PARTIALLY REFLECTIVE WALLS

The results of a recent study in 2010,van Groesen et.al [3] found the new water waves equation, known as

AB2-equation, which describes the nonlinear dispersive waves which travel mainly in one direction. The AB2- equation is variational derivation of improved Kadomtsev-Petviashvili equation and valid for the waves on deep water.We will solve numerically the equation by spectral methods.The advantages of this equation that has the exact dispersion relation and is exact up to second order of the wave height. We interest to learn the AB2-equation because this equation is relatively new.Moreover,studying the wave generation problem by using this equation. In AB2-equation, the waves generated on the boundary be considered as an inhomogeneous boundary conditions or an influx. Using spectral methods, the problem with inhomogeneous boundary conditions are not easy to perform.

However, this problem has been studied by Lie in 2010 [4]. In his study, Lie using Duhamel principle to convert the inhomogeneous boundary condition into external force on the equation with homogeneous boundary conditions.The source function for the wave influxing in Lie’s study is derived base on the linear theory.Then,Lie has done the simulation by taking the data from MARIN as the influx and compared his simulation with the MARIN measurments. Based on research conducted by Lie, we interest to verify the solution of AB2-equation with soliton profile as the solution. To understand this equation, we begin the verification by doing the simulation.We take previously the linear part of AB2-equation and the simple harmonic waves as an influx.After that, we use Lie’s model to generate this waves with an angle. In the simulation,we take firstly a simple harmonic wave as the influx with the angle is zero. Secondly, we generate a combination of two simple harmonic wave to see the effect of dispersive properties. Then, we do the simulation for a simple harmonic waves with the angle -30 degrees and 30

degrees.Futhermore,we generate two waves with different angle and we can see the collision of two waves.

In addition,we try to generate a wave that has soliton profile.

LIST OF RESEARCH OUTPUT

1. L. Yuliawati,Wono Setya Budhi,J.M Tuwankotta,Simulation For Linear Obloque Waves in 2D,

Proceedings ICMNS 2014.

2. Natalia, Wono Setya Budhi, and E. van Groesen, Solving Laplace Equation With Mixed Boundary

Condition for Ship Problem in The Sea Using Pseudo-Differential Operator,Proceedings ICMNS 2014.

3. Fitriani Tupa R. Silalahi,Wono S. Budhi, Didit Adytia, E. van Groesen, Numerical Solution for Laplace

Equation with Mixed Boundary Condition for Ship Problem in the Sea,Proceedings ICMNS 2014.

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HEAD OF RESEARCH TEAM : Prof.Wono Setya Budhi, Ph.D

OFFICIAL ADDRESS : Faculty of Mathematics and Natural Sciences, lnstitut Teknologi

Bandung, Jl. Ganesha 10, Bandung

EMAIL : wono@math.itb.ac.id

Prof.Wono Setya Budhi, Ph.D