Isothermal/thermal incompressible viscous fluid flows with the velocity-vorticity formulation

Numerical results in two dimensions for isothermal/thermal flows of viscous incompressible fluids mathematically modeled by the Navier-Stokes equations and the Bousssinesq approximation are presented in the velocity-vorticity formulation. The thermal flows correspond to natural and mixed convection. The results are obtained based on a fixed point iterative process for solving the nonlinear elliptic system that results after an appropriate time discretization is made. The iterative process leads to the solution of uncoupled, well conditioned linear elliptic problems for which very efficient solvers are known to exist regardless of the space discretization.