Lagrangian Formulations to Solve Free Surface Incompressible Fluid Flows

Abstract

A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used in ``meshless´´ approximations and the time integration is introduced in a semi-implicit way by a fractional step method. In this manner, both classical stabilization terms used in incompressible Euler equations are unnecessary: numerical diffusion for convective terms are unnecessary due to the Lagrangian formulation, and stabilization of pressure due to the incompressibility constraint for equal order interpolations is eliminated using the fractional step method.