Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic The float glass process (Pilkington process) is the standard industrial scale process for manufacturing flat glass. The first phase of the process is the flow of the glass melt down an inclined plane (spout), and its impact on the tin bath, which makes the process a practical example of a multicomponent physical system. Our objective is to develop a mathematical model for the process, and implement a numerical scheme that would allow us to perform computer simulations of the process. For the numerical simulations we use a Cahn-Hilliard-Navier-Stokes type model which conceptually belongs to the class of so-called diffuse interface models. These models treat the interface between the components as a thin layer across which the components can mix, and that, among others, automatically take into account the surface tension effects. This allows one to avoid highly specialized and difficult to implement interface tracking methods. The cost to pay is the need to use a very fine spatial resolution in particular at the interface between the components. We will discuss the numerical challenges that must be addressed in order to make the numerical simulations based on the Cahn-Hilliad-Navier-Stokes type model applicable in the modelling of Pilkington process.