In this simulation the left boundary is kept at one degree higher temperature than the right boundary. On the top boundary the variations of surface tension due to temperature differences on the surface induce a tangential force on the flow. This effect is called thermocapillary convection or Marangoni convection.
The flow was assumed incompressible. The ElmerSolver uses a stabilized finite element formulation to solve the incompressible Navier-Stokes equations and heat equation with the convection term. In this simulation linear triangular finite elements were used. The coupled system was solved by the method of sequential iteration.
If you want to reproduce the results, download the file Marangoni.tar.gz and follow the instructions in the file README. You should have the Elmer package installed in your computer, however.
The figures show the velocity vectors
and the temperature field at steady state.