The characteristic variational multiscale method for time dependent conduction-convection problems

In this paper, the characteristic variational multiscale (C-VMS) method is proposed to solve the nonstationary conduction-convection problems. The stability analysis is carried out using the energy estimate method. Compared with the standard variational multiscale (VMS) method, the C-VMS method does not need nonlinear iteration. Finally, some numerical examples are given, which show that the C-VMS method is efficient, reliable and can save a lot of CPU time for this problem, besides, it can deal with the high Rayleigh number.