A MASS-CONSERVING SMOOTH METHOD

Abstract

Curve/surface smoothing is a problem that appears in different fields, such as computer
graphics and computational fluid mechanics. In fluid flow simulation with free surface,
particularly when the Reynolds number is high, small undulations may appear at the free surface
due to variations in the velocity field from cell to cell. These undulations are frequently
much smaller than a cell size and a numerical implementation that acts at cell level cannot
take into account these sub-cell undulations, being necessary suppress them. There are several
approaches that can be used to smooth these unphysical undulations, such as Gaussian filter.
However, in fluid flow simulations it is important that the smoothing process keeps the mass (or
volume) unchanged. In this work we present a smoothing technique that suppresses undulations
while still conserving the mass. The approach consists in computing a local volume which
is preserved during the smoothing process. The results of applying such technique in planar,
axisymmetric, and three-dimensional free-surface flows are presented and discussed.