On some practical issues concerning the implementation of Cahn–Hilliard–Navier–Stokes type models

  • Martin Řehoř
  • Jan Blechta
  • Ondřej Souček


Suspensions, solutions and colloids are physical systems that can be generally denoted as “multicomponent systems” or “mixtures”. Physical systems of this type are frequently met in many industrial applications which rises the need for numerical simulations of the behaviour of such complex systems. A particular practical example of such system is glass/tin/nitrogen system that must be studied in modelling of the float glass process (Pilkington process) that partly motivated this research. The aim of this paper is to discuss the numerical challenges along with some practical issues concerning the implementation of a chosen Cahn–Hilliard–Navier–Stokes type model that showed up to be particularly suitable for the description of three-component systems. The discretization of the system of governing partial differential equations is based on the finite element method using the FEniCS Project. Numerical experiments carried out in two and three spatial dimensions verify our straightforward implementation that uses parallel direct sparse solvers to resolve the intermediate linear systems of algebraic equations. Possible improvements of the current implementation are briefly outlined within the paper.


Multicomponent flows Cahn–Hilliard–Navier–Stokes model Finite element method 

Mathematics Subject Classification

76T30 76D05 65M60 



Support of Glass Service (an advanced solutions supplier in the field of glass melting, conditioning and forming) is gratefully acknowledged.


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Copyright information

© Indian Institute of Technology Madras 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPraha 8 – KarlínCzech Republic

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