Two-dimensional thermal convection flow with variable viscosity and embedded boundaries

Abstract

A two-dimensional model capable of simulating thermal convection flow in complex geometries has been implemented in a finite-difference setting and using a fictitious domain method of type “direct explicit forcing". The Boussinesq approximation is supposed to hold; the coupling between velocity and temperature fields is explicit; spatially varying viscosity is accounted for. The computation of a model for the thermally-induced flow in a three-chamber fuel tank reveals that the present method does not allow for sufficiently large time steps when the viscosity varies strongly.