Effect of local property smearing on global variables: Implication for numerical simulations of multiphase flows

This work addresses the sensitivity of a calculated global quantity to the smoothing of discontinuous variation of properties. The analysis is based on the very simple model problem of a fully developed, thermocapillary channel flow. The predictions of this simple model are shown to be in excellent agreement with the results for the Navier-Stokes simulations of the thermocapillary migration of a spherical drop. The main conclusion is that the migration velocity depends very strongly on the smearing of the driving interfacial force whereas it is rather insensitive to the smearing of the discontinuous viscosity distribution. This hints at the indispensability of grid adaption for modeling interfacial forces.