The three-dimensional Eulerian–Lagrangian marker and micro cell method for the simulation of free surface flows

A new method is presented for the simulation of three-dimensional, incompressible, free surface fluid flow problems. The new technique, the Eulerian–Lagrangian marker and micro cell (ELMMC) method, is capable of simulating incompressible fluid flow problems in Cartesian coordinates where the free surface can undergo severe deformations, including impact with solid boundaries and impact between converging fluid fronts. The method is also capable of handling the breakup of a fluid front from the main body of the fluid as well as their eventual coalescence. The basic solution methodology solves the continuity and the Navier–Stokes equations with a projection scheme and is even able to incorporate a basic k–ε turbulence modeling capability. New approaches are presented for the advection of the free surface, as well as for the calculation of the tentative velocity, final velocity, and pressure fields. The capabilities of the new method are demonstrated by comparing numerical results with experimental studies while the convergence of the new method is demonstrated by spatial and temporal refinement studies.