I am calculating 2D problem with free surface which is captured by level set method.In level set method the density near interface changes smoothly.Now I want to use Roe scheme for convective terms but because of the change of density the NS equation has to be written as conservative form.I can not use ros's directly.But we have some codes based on roe's schem.So would you please give me some suggestions about what I should do!Thank you!

Anyone who is engaged in free surface problem using Finite Volume Method,please contact with me!

The Roe scheme is for hyperbolic systsem which is usually written in conservative form. Q_t+ F_x=0. How to apply Roe scheme to nonconservative, convective term?

If you are considering one fluid and impressible problem just keep density outside or nondimensionalize the N-S equation.But for me there are free surface between the air and water I have to use conservative form to include the density change especially for level set.And roe can be used for nonconservative form i think.If any questions please continue leacing your message.