We present special numerical simulation techniques for non-isothermal incompress-
ible viscous fluids. The flow which is governed by the Boussinesq approximation and
the Navier-Stokes equations is solved in a fully coupled monolithic way. For time
discretization, we apply the fully implicit Crank-Nicolson scheme of 2nd order ac-
curacy. We utilize the high order Q2P1 finite element pair for discretization in space
to gain high accuracy with local grid refinement. The resulting nonlinear discrete
systems are solved via a quasi-Newton method with a divided difference approach
to handle the Jacobian matrices. In each nonlinear step, the discrete linear sub-
problems are solved by means of a special multigrid method with local multilevel
pressure Schur complement smoothers. For validation of the presented methodology,
we perform the MIT benchmark 2001 [3, 4] of natural convection flow in enclosures
to compare our results with respect to accuracy and efficiency. Additionally, we
simulate problems with temperature and shear dependent viscosity and discuss the
effect of an additional dissipation term inside the energy equation.