Novel hybrid compact schemes for stream function-velocity formulation of the incompressible Navier-Stokes equations

In this paper, we have developed new hybrid compact schemes for the simulation of stream function-velocity formulation of the two-dimensional incompressible Navier-Stokes equation. The first-order spatial derivatives are approximated by the optimized upwind compact scheme, and the Laplacian and biharmonic operators are discretized using fourth-order hybrid compact schemes. Moreover, we have also performed Fourier analysis to assess the resolution and added numerical diffusion properties of numerical schemes for stream function-velocity formulation of the linear Navier-Stokes equation. For time discretization, we have used explicit fourth-stage fourth-order Runge-Kutta method and hybrid filters. Furthermore, to validate the accuracy and efficiency of the schemes, several fluid flow problems, including a test problem with a non-homogeneous source term and a lid-driven cavity problem, are considered. Numerical results exhibit a great match to the results reported in the literature at lower computational cost with hybrid filters.