Numerical Simulation of Solitary Wave Using the Fully Lagrangian Method of Moving Particle Semi Implicit

A mesh-less numerical approach, called the moving particle semi implicit method (MPS), is presented to solve inviscid Navier-Stokes equations in a fully Lagrangian form using a fractional step method. This method consists of splitting 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. In this paper, the MPS method is used to simulate a dynamic system consisting of a heavy box sinking vertically into a water tank, known as Scott Russell’s wave generator problem. This problem is an example of a falling rock avalanche into natural or artificial reservoirs. The box sinks into water tank and as a result the water is heaved up to form a solitary wave and a reverse plunging wave which forms a vortex. This vortex follows the solitary wave down the water tank. The good agreement between the numerical simulation and the analytical solution confirms the accuracy of the model. This proves the applicability of the present model in simulating complex free surface problems. The number of particles on free surface is presented as an indicator of stability of the model.