A numerical method for solution of incompressible Navier–Stokes equations in streamfunction-vorticity formulation

In this work, we have proposed a numerical approach for solving the incompressible Navier–Stokes equations in the streamfunction-vorticity formulation. The numerical scheme is based on the diagonally implicit fractional-step $\theta -$(DIFST) method used for the time discretization and the conforming finite element method for the spatial discretization. The accuracy and efficiency of the scheme are validated by solving some benchmark problems. The numerical simulations are carried out using the DUNE-PDELab open-source software package. The comparison of DIFST scheme with different time discretization schemes is provided in terms of CPU time. Also, different solvers with preconditioners are investigated for solving the resulting algebraic system of equations numerically.