V. Sass et al., INVESTIGATION OF 3-DIMENSIONAL THERMOCAPILLARY CONVECTION IN A CUBIC CONTAINER BY A MULTIGRID METHOD, International journal of heat and mass transfer, 39(3), 1996, pp. 603-613
Three-dimensional thermocapillary convection of a Boussinesq fluid in
an open cubic container is considered in the absence of buoyancy. The
steady motion is computed with a modified Full-Approximation Scheme, F
ull Multi-Grid (FAS-FMG) method based on a finite difference, primitiv
e variable formulation. Solutions on a staggered grid of 32 x 32 x 32
points for each unknown are obtained by a line coupled, block implicit
relaxation method for the Navier-Stokes equation, and an alternating
zebra-relaxation method for the energy equation. Three-dimensional (3D
) flow structures and temperature fields are presented for Reynolds nu
mbers up to 5 x 10(4) and Prandtl numbers Pr = 0.01, 1, 10 and 50. Apa
rt From the main vortex known from 2D calculations pronounced secondar
y vortices appear. The mechanisms driving this secondary how are discu
ssed in terms of well-known properties of the main vortex.