Stable Moving Particle Semi Implicit Method for Modeling Waves Generated by Submarine Landslides

A mesh-free numerical formulation, known as Moving Particle Semi Implicit (MPS) Method, is used for modeling waves generated by submarine landslides. In this formulation, approximations are provided to the strong form of PDEs on the basis of integral interpolants. The governing equations, Navier-Stokes equations, are solved in a 2D fully Lagrangian form. This method utilizes a fractional step method and splits each time step in two steps. The fluid is represented with particles and the motion of each particle is calculated through interactions with neighboring particles by means of a kernel function. Landslides in this paper are simulated by a submerged triangle rigid wedge sliding along an inclined plane into a water tank. As the wedge sinks, a wave and a vortex is formed. The water surface profile, velocity field and pressure field are represented at different times. To confirm the accuracy of the model, the water surface profile is compared with the experimental data, showing good agreement. Simulations can continue for a long period of time without any instability occurrence and this is a remarkable competency amongst other particle methods. A discussion on multi-size particle strategy and its ability to increase the efficiency of MPS method is provided at the end of the paper.