A second order characteristics finite element scheme for natural convection problems

In this paper a second order characteristics finite element scheme is applied to the numerical solution of natural convection problems. Firstly, after recalling the mathematical model, a second order time discretization of the material time derivative is introduced. Next, fully discretized schemes are proposed by using finite element methods. Numerical results for the two-dimensional problem of buoyancy-driven flow in a square cavity with differentially heated side walls are given and compared with a reference solution.