Often after the simulation has
 

Often after the simulation has started, I find that the minimum volume fraction for a certain phase has a negative value which I guess comes from using the limitedLimitedLinear scheme. For instance, here is a transcript of the log file:

Courant Number mean: 0.0003676463941223166 max: 0.1433804123149916
deltaT = 5.902777777777798e-05
Time = 0.01246875

smoothSolver: Solving for alphawater, Initial residual = 5.367012678397666e-07, Final residual = 1.657007202694921e-09, No It
erations 1
water volume fraction, min, max = 0.500000013666753 -2.476129830158727e-05 1.000241328781609
smoothSolver: Solving for alphaoil, Initial residual = 0.0005141524902777194, Final residual = 1.115623990538466e-09, No Iter
ations 3
oil volume fraction, min, max = 0.001774934415791225 -0.0002436711866175406 1.000002660725418
air volume fraction, min, max = 0.4982250519173831 -0.0001213547565864747 1.000021713925952

Is there a way to prevent negative volume fractions such as -0.0002436711866175406 and -0.0001213547565864747 by using a different scheme? Or would grid refinement cause the problem to go away?

My current fvSchemes file reads:

ddtSchemes
{
default Euler;
}

gradSchemes
{
default Gauss linear;
grad(U) Gauss linear;
grad(gamma) Gauss linear;
}

divSchemes
{
div(rho*phi,U) Gauss upwind;
div(phi,alpha) Gauss limitedLimitedLinear 1.0 -0.00001 1.00001;
div(phic,alpha) Gauss interfaceCompression; //upwind;
}

laplacianSchemes
{
default Gauss linear corrected;
}

interpolationSchemes
{
default linear;
}

snGradSchemes
{
default corrected;
}

fluxRequired
{
default yes;
}