Generation and propagation of a Tsunami wave : a new mesh adaptation technique

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.