A fully mesh-less Lagrangian numerical method for prediction of free water surface

Euler's equation is the governing equation of the irrotational flow of ideal fluids; this equation can be considered for the free surface water flow in open channels. The two dimensional Euler's equation is solved by a mesh-less method of Smooth Particle Hydrodynamics (SPH). A fractional step method has been applied which consist to split each time step in two steps. The numerical method is based on 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. The numerical model results are verified with the available experimental results for the collapse of a water column. Agreement with experimental results is excellent. Finally the effect of height of dam and the kernel size on the time the bore is formed is investigated and an estimate for the time of bore formation is presented. The present model is a very useful utility for solving problems in hydraulic and river engineering that an accurate prediction of free water surface is required.