Change in coefficients
 

Hello, I am solving the Unsteady Convection-Diffusion eq. with variable coefficients on the form:

C1*dU/dt+ d/dx[C2*u*U]=d/dx[C3*dU/dx]

the coefficients very sensitive to the value of U, i.e. C's=fnc(U). This makes my code fail to converge. What I am using is upwind finite difference to Convection term and Central difference to Diffusion term (implicit scheme). At each time step, as an attempt to reach a converged solution, I hold the time and try to make a series of Iteration in order for solution to converge on this form:

C1=(1-UR)*C1(Previous) + UR*C1(Current)

where UR-under-relaxation parameter. But I failed with different values of UR {0.001<UR<1} Any suggestion would be appreciated.