In Reynolds stress models (RSM), the use of first gradient closures to model diffusion fluxes may lead to a nonconvergence with mesh refinement, especially if the flow experiences episodes of dominant compressibility effects like during interactions with shock waves. In our turbulence mixing model, we have implemented two methods to prevent the divergence of these fluxes inside shocks. They are based on the use of Schwarz inequalities and on the detection of zones where compressibility effects are the dominant source of turbulence. The necessity of a specific adjustment and the efficiency of the method are demonstrated in the case of shock interaction with homogeneous turbulence. The sensitivity of the results in the more practical case of mixing zones generated in shock tubes is illustrated.