Iteration penalty method for the incompressible Navier-Stokes equations with variable density based on the artificial compressible method

Based on the artificial compressible method, an iteration penalty semi-discrete scheme is proposed for the numerical simulations of the incompressible Navier-Stokes equations with variable density. Compared with the classical penalty scheme, the main feature is that the proposed iteration penalty scheme is of the first-order temporal convergence rate for any penalty parameter epsilon > 0 independent of the time step size tau. Numerical results are given to illustrate the theoretical analysis.