Investigation of three-dimensional thermocapillary convection in a cubic container by a multi-grid method

Abstract

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, Full Multi-Grid (FAS-FMG) method based on a finite difference, primitive variable formulation. Solutions on a staggered grid of 32 × 32 × 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 numbers up to 5 × 10 4 and Prandtl numbers Pr = 0.01, 1, 10 and 50. Apart from the main vortex known from 2D calculations pronounced secondary vortices appear. The mechanisms driving this secondary flow are discussed in terms of well-known properties of the main vortex.