Influence of Integration Schemes of Surface Movement in Numerical Simulation of Free Surface Problems

Abstract

In this work, we analyze the influence of different time integration schemes for surface movement tracking inside an Arbitrary Lagrangian Eulerian approach to free surface problems. Based
in a known unconditional instability present in the classical explicit scheme, we propose a little bit more sophisticated one based in Runge Kutta method that's provide a conditional stable behavior and low diffusivity compared with a full implicit algorithm, for a pure transport problem. Also, we show that for a Navier Stokes fluid model under gravity waves condition; the influence of the free surface integration rule could be hidden by the numerical treatment of bulk fluid.