Meshless modeling of submarine landslide generated fully nonlinear waves and runup

Abstract

A two-dimensional numerical model based on fully nonlinear potential ow theory is proposed for the simulation of tsunamis generated by earthquakes and submarine landslides. The boundary value problem of the theory is numerically solved using the method of fundamental solutions which is a boundary only method. Thus, the model can cope with large domains which are required for the modeling of the long distance propagation of tsunamis. Because of the singular nature of the fundamental solution, the approximating functions are de ned on the ctitious boundaries located parallel to the physical boundaries. The positions of the ctitious boundaries are updated at each time level to avoid any numerical instability that may be caused by the closeness of the physical and the ctitious boundaries. The tsunami generation mechanism in the model is based on bottom deformation whose motion can be described by a water depth function or by a time dependent velocity eld with the initial geometric properties of bottom. Time dependent deformations both on the bottom and on the free surface are easily implemented in the model thanks to the meshless feature of the method. Using the full-Lagrangian description of the deforming free surface, the run-up and the run-down of waves can be accurately modeled by the model without any additional technique. Moreover, three di erent tsunami generation benchmark problems are simulated using this description. The accuracy of a second description of the free surface which is called semi-Lagrangian is tested for the simulations of earthquake generated tsunamis. The results obtained using the present model are compared with those of other well known models and with experimental measurements. The comparisons demonstrated the accuracy and the reliability of the model for the simulations of tsunami generation, propagation and run-up.