Multilevel finite volume methods for 2d incompressible navier-stokes equations

In this work, implicit and explicit multilevel finite volume methods have been constructed to solve the 2D Navier-Stokes equation with specified initial condition and boundary conditions. The multilevel methods are applied to the pressure-correction projection method using space finite volume discretization. The convective term is approximated by a linear expression that preserves the physical property of the continuous model. The stability analysis of the numerical methods have been discussed thoroughly by making use of the energy method. Numerical experiments exhibited to illustrate some differences between the new (multilevel) and conventional (one-level) schemes.