A projection FEM for variable density incompressible flows

This work describes a new finite element projection method for the computa-tion 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 ver-sion of the projection method is possible provided two projections are performed per time step. In particular, a second order accurate BDF projection method is pre-sented and its numerical performance is illustrated by test computations and comp-arisons. c ° 2000 Academic Press Key Words: variable density Navier–Stokes equations; incompressible flows of nonuniform density; fractional step projection method; poisson pressure equation; incremental second order projection method; BDF scheme; finite elements; mixed method. 1