A Second-Order Projection Method for Variable-Density Flows

This paper describes a second-order projection method for variable-density incompressible flows. The method is suitable for both finite amplitude density variations and for fluids that are modeled using a Boussinesq approximation. It is based on a second-order fractional step scheme in which diffusion-convection terms are advanced without enforcing the incompressibility condition and the resulting intermediate velocity field is then projected onto the space of discretely divergence-free vector fields. The nonlinear convection terms are treated using a Godunov-type procedure that is second order for smooth flow and remain stable and non-oscillatory for nonsmooth flows with low fluid viscosities. The method is described for finite-amplitude density variation and the simplifications for a Boussinesq approximation are sketched. Numerical results are presented that validate the convergence properties of the method and demonstrate its performance on more realistic problems.