Didit Adytia

Variational Boussinesq model for simulation of coastal waves and tsunamis

In this paper we describe the basic ideas of a so-called Variational Boussinesq Model which is based on the Hamiltonian structure of gravity surface waves. By using a rather simple approach to prescribe the profile of vertical fluid potential in the expression for the kinetic energy, we obtain a set of dynamic equations extended with one additional elliptic equation for the amplitude of the vertical profile. All expressions in the energy contain at most first order derivatives, which makes a numerical implementation with finite elements relatively easy. The applicability of the code is illustrated for two different applications in this paper. One application deals with tsunami simulations, for which we show the phenomenon of tsunami waveguiding before the coast of Lampung in Indonesia. Another application deals with simulations of coastal waves entering the small harbour of Cilacap on the south-coast of Java, Indonesia; we will show that the simulations indicate a resonance phenomenon in the small inner harbour.

Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea

One interesting phenomena is investigating the movement of ships at the sea. To start with the investigation in modelling of this problem, we will assume that the ship is only a one-dimensional object that is floating on the sea surface. Similarly, we assume that the water flow is uniform in parallel directions to the ship. Therefore, we simply use the two-dimensional Laplace equation in this problem. In the section that describes the surface of sea, Neumann boundary condition is imposed in part related to the ship and the Dirichlet boundary condition for others. Then on the other three boundaries, we imposed the Neumann boundary condition by assuming that the water does not flow on the bottom, and both end. The model is solved by numerical solution using the finite element method. Velocity potential solution on the whole domain is demonstrated as a result of the implementation of the finite element method. In this paper, we initiate an investigation with assuming that the ship is on the water so that the domain of the Laplace equation is rectangular. Then we assume the drift ship. Furthermore, we also study the dependence of width and depth of the domain to the velocity potential.

Wave run-up of a possible Anak-Krakatau tsunami on planned and optimized Jakarta Sea Dike

The infrastructural plans in the Jakarta Bay to reduce risks of flooding in Jakarta city comprise a large Sea Dike that encloses a retention lake. Part of the planned dike has the shape of the iconic Garuda bird. This paper shows that if in the future an explosion of Anak Krakatau will occur with strength 1/4th of the original Karkatau 1883 explosion, wave crests of 11m and troughs of 6m may collide against the bird’s head. As an alternative example, a more optimized design of the dike is constructed that reduces the maximal wave effects considerably.

Simulation of obliquely interacting solitary waves with a hard wall by using HAWASSI-VBM and SWASH model

In this paper we discuss the comparison of numerical simulations of solitary waves, reflected from a rigid wall under an angle, using the HAWASSI-VBM (Hamiltonian Wave-Ship-Structure Interaction – Variational Boussinesq Model) and the SWASH (Simulating Waves ‘till Shore) model. We reconstruct the experiment of Yeh et al (2011) to investigate the amplification of the Mach stem phenomenon. In the simulation, some solitary waves from the solution of Kadomtsev-Petviashivili (KP) equation with the angle of 30° is chosen as the incident wave. We compare the results of numerical simulation with the laboratory experiment of Yeh et al. Based on this comparison, results of numerical simulation from both wave models show a quite good agreement with the experiment data.