Effects of Numerical Treatment of Viscous and Surface Tension Forces on Predicted Motion of Interface

Abstract

Effects of numerical treatment of viscous and surface tension forces on predicted motion of an interface are investigated. The viscous force and tangential surface tension force (Marangoni force) are treated in two different ways: one is a smeared-out interface method and the other is a ghost fluid method. In the smeared-out interface method, the arithmetic mean and harmonic mean are tested for evaluation of the viscous stress. Linear shear flows, single oscillating drops and surface tension waves are simulated using these methods. These benchmark tests show that the ghost fluid method gives the most accurate evaluations of the viscous and the Marangoni forces. The harmonic mean can give good evaluations of the tangential viscous stress at clean interface, whereas large errors in the viscous stress are caused for contaminated interface. Although the arithmetic mean causes some errors for clean and contaminated interfaces compared to the ghost fluid method, the error can be reduced by increasing spatial resolution and this method can give more reasonable predictions for contaminated interface than the harmonic mean. The arithmetic mean is therefore recommended rather than the harmonic mean when using the smeared-out interface method.