Journal of Mathematics in Industry

, 2:1

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Numerical simulation of thin paint film flow

  • Bruno FigliuzziAffiliated withCentre de Morphologie Mathématique, École des Mines ParisTech Email author 
  • , Dominique JeulinAffiliated withCentre de Morphologie Mathématique, École des Mines ParisTech
  • , Anaël LemaîtreAffiliated withUMR Navier
  • , Gabriel FricoutAffiliated withArcelorMittal Global R&D
  • , Jean-Jacques PiezanowskiAffiliated withArcelorMittal Global R&D
  • , Paul MannevilleAffiliated withLadHyX, École Polytechnique



Being able to predict the visual appearance of a painted steel sheet, given its topography before paint application, is of crucial importance for car makers. Accurate modeling of the industrial painting process is required.


The equations describing the leveling of the paint film are complex and their numerical simulation requires advanced mathematical tools, which are described in detail in this paper. Simulations are validated using a large experimental data base obtained with a wavefront sensor developed by Phasics™.


The conducted simulations are complex and require the development of advanced numerical tools, like those presented in this paper.


thin films numerical simulation industrial painting process roughness lubrication approximation