I have used a SIMPLE code with the introduction of the source terms for a solidification problem. The problem is that my flow has variable density which is a function of temperature, when the solid forms, the axial velocity becomes nearly zero (based on my source term value), however the radial velocity does not change. I have tried different values but it it not working. Also the axial velocity becomes negative in certain positions (pressure in the cell is positive but less than the following cell pressure). Can anyone help me with a hint or maybe a different method to overcome this problem?

This causes the temperature to increase in the axial direction (in the solid part and the order of increase is in 10^-3C). Thanks a lot for your help!

Is it the 'enthalpy method'? Are you taking care of the latent heat release properly?

Yes I am using the Enthalpy method. The issue is that the axial velocity is large before solidification (say 10^-3m/s) and then it drops to 10^-10 due to solidification and the source term in the momentum equation, however the radial velocity remains in the same order (10^-7).