compressibility correction for S-A turbulent Model

autofly

I try to add the Compressibility correction terms " -C5*(Vt)^2/(a*a)*Uij*Uij " to the source terms as Paper AIAA 2002-0586. Now i meet the basic difficulty in defing the Uij*Uij in my fortran code. first , what 's the meaning of Uij second, how to expand the Uij*Uij in detailed formula but no in concise form" uij*uij who can provide me the details about the correction ? thanks in advance