Filtering for singularities in a Marangoni problem
2006 - H. Herrero, A.M. Mancho, S. Hoyas
Numerical Mathematics and Advanced Applications, ENUMATH 2005, 889-896 (2006).
Herrero Sanz, Henar.
The problem considered consists of a fluid within a cylindrical annulus heated laterally. As soon as a horizontal temperature gradient is applied a convective state appears. This state becomes unstable through stationary or oscillatory bifurcations as control parameters involved in the problem reach critical values. The problem is modelled with the incompressible Boussinesq Navier-Stokes equations and appropriate boundary conditions. In particular we consider lateral conducting walls and surface tension effects. This choice presents singularities at the point where free and solid surfaces meet, which consist on discontinuities on the temperature and its derivatives. These singularities are smoothed using a polynomial filtering. The main goal of this work is the study of the effect of this filtering in the stability problem. The filter improves the convergence of the numerical method. Convergence with the filtering scale depends on the Marangoni parameter.