A Projection FEM for Variable Density Incompressible Flows

This work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density. One original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation, to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid. It is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step. In particular, a second order accurate BDF projection method is presented and its numerical performance is illustrated by test computations and comparisons.