@TechReport{ it:2009-026,
author = {Sara Zahedi and Martin Kronbichler and Gunilla Kreiss},
title = {Spurious Currents in a Finite-Element Based Level Set
Method for Two Phase Flow},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2009},
number = {2009-026},
month = nov,
abstract = {A study of spurious currents in finite element based
simulations of the incompressible Navier-Stokes equations
for two phase flows is presented, based on computations on
a circular drop in equilibrium. The interface is accounted
for by a level set method. It is shown that a sharp surface
tension force, expressed as a line integral along the
interface, can give rise to large spurious currents and
oscillations in the pressure. If instead a regularized
surface tension representation is used, exact force balance
at the interface is possible, both for a fully coupled
discretization approach as well as for a fractional step
projection method. We illustrate that with exact force
balance, the spurious currents are of the order of the
tolerance of the linear solver. However, the numerical
curvature calculation introduces errors, that cause
spurious currents. Different ways to extend the curvature
from the interface to the whole domain are discussed and
investigated. It is shown that the choice of curvature
extension has a significant impact on the error in
pressure. The impact of using different finite element
spaces is also investigated.}
}