 
Summary: 1
VARIATIONAL BOUSSINESQ MODEL FOR SIMULATION OF
COASTAL WAVES AND TSUNAMIS
DIDIT ADYTIA
E. VAN GROESEN
LabmathIndonesia, Lawangwangi, Bandung, Indonesia
& Applied Mathematics,University of Twente, Enschede, Netherlands
In this paper we describe the basic ideas of a socalled 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 southcoast of Java, Indonesia; we will show that the simulations
indicate a resonance phenomenon in the small inner harbour.
1 Introduction
Coastal zones around the world are important because already from long times ago these
