A comparison study of the Boussinesq and the variable density models on buoyancy-driven flows

When density variations are sufficiently small the Boussinesq approximation is valid. The approximation is introduced to reduce the degree of the complexity of density variations and implies that density effects are considered only in the buoyancy force term of the momentum equation. Because of its simplicity in practical implementations, the approximation is widely used. Although there are many studies related to the approximation, some important characteristics are still missing. In this article, we compare the Boussinesq approximation and variable density models for the two-dimensional (2D) Rayleigh-Taylor instability with a phase-field method. Numerical experiments indicate that for an initially symmetric perturbation of the interface the symmetry of the heavy and light fronts for the Boussinesq model can be seen for a long time. However, for the variable density model, the symmetry is lost although the flow starts symmetrically.