  The importance of the study of the propagation of a Tsunami wave came from
the complex phenomenon and its natural disasters which represents a major risk
for populations. To model this phenomena, we will consider a simplified
Boussinesq system of Benjamin, Bona and Mahony type derived by D. Mitsotakis
over a flat bottom then over a variable bottom in space and in time and apply
this system, first, using a mesh generated using a photo of the Mediterranean
sea, second, using a mesh generated using an imported xyz bathymetry for the
sea near Java island and then we will consider a realistic example of the
Tsunami wave near Java island which happened in 2006.We choose here to use
FreeFem++ software which simplifies the construction of the domain, in
particular, one of the advantage of FreeFem++ is that we can build a mesh using
a photo and we can easily export bathymetric data in order to consider more
realistic simulations where a special adapt mesh technique applied for these
two methods is detailed in the sequel.
