A passive scalar is a property that is affected by the flow field without affecting it. In this paper, first, the governing equations on the turbulent flows are solved and the property of a passive scalar in two dimensions is numerically studied. Having the values of the velocity components, the governing equation on transport of a passive scalar is solved. To compute the turbulent velocity field, the Large Eddy Simulation (LES) method using Smagorinsky subgrid scale is invoked. The flow in a cavity has been the basis to validate the accuracy of the generated computer code. To ensure the compatibility between the flow and the transport of passive scalar fields a similar LES approach is used. As a three-dimensional numerical solution for a turbulent flow fields needs a massive computational time and efforts, therefore a two-dimensional simulation used for a proper saving. Instead, to validate the numerical results, the range of the Reynolds number of the flow is kept within the range of the two-dimensional measurements. Comparison of the numerical results and the experimental measurements in two-dimension reveals the high accuracy of the results and compatibility between the flow and passive scalar fields. Ability of developed scheme to accurately handle transport of a passive scalar is promising to extend LES method into the transport of more species and hence to simulate reacting flows.