Numerical simulation of mixed convective flow and heat transfer in a staggered double lid driven cavity using Newton-multigrid FEM

A computational study has been carried out for the analysis of two dimensional, incompressible and steady mixed convective flow and heat transfer in a staggered double lid driven cavity. The resulting system of equations is discretized using Galerkin finite element method and in particular, the LBB-stable finite element pair Q₂/P₁^disc which lead to 3rd and 2nd order accuracy in the L₂-norm for the velocity/temperature and pressure, respectively. The discrete system of nonlinear equations is treated with the help of Newton’s method and the corresponding linear systems are treated using monolithic geometric multigrid solver with Vanka-type smoother.