In this paper we studied mathematical models for fluid flow often involve systems of convection-diffusion equations as a main ingredient. Operator splitting - one splits the time evolution into partial steps to separate the effects of convection and diffusion. In the present paper it has been shown that that the temporal splitting error can be significant when there is a shock present in the solution, is well-understood for scalar convection – diffusion equation. Keywords: Convection diffusion, convection solver, front tracking method, nonlinear error mechanism, operator splitting
