Improved MPS method for simulating water flow with irregular free surface

Euler's equation is the governing equation of the irrotational flow of ideal fluids; this equation can be considered for free surface water flow in open channels. The Euler's equation, is solved by a mesh-less method. Also a fractional step method is applied which consists in splitting each time step in two steps. This numerical method is based on the Moving Particle Semi implicit method (MPS) for simulating incompressible inviscid flows with free surfaces. The motion of each particle is calculated through interactions with neighboring particles covered with the kernel function. In spite of the extensive applications of MPS method, still there are limitations for getting a stable solution by this method. In this paper various kernel functions are considered and applied to improve the stability of MPS method. Based on these studies a new kernel function is introduced that improves the stability of MPS method. The numerical results of the model are verified with the available experimental results for the collapse of a water column. Agreement with experimental results is excellent. The applicability of this model to simulate hydraulic problems with free surface is shown through the solution of further examples. The present model is a very useful utility for solving problems with irregular free surface in hydraulic and coastal engineering when an accurate prediction of free water surface is required.