Decoupled scheme for time-dependent natural convection problem. II: Time semidiscreteness (Q1719033)

Summary: We study the numerical methods for time-dependent natural convection problem that models coupled fluid flow and temperature field. A coupled numerical scheme is analyzed for the considered problem based on the backward Euler scheme; stability and the corresponding optimal error estimates are presented. Furthermore, a decoupled numerical scheme is proposed by decoupling the nonlinear terms via temporal extrapolation; optimal error estimates are established. Finally, some numerical results are provided to verify the performances of the developed algorithms. Compared with the coupled numerical scheme, the decoupled algorithm not only keeps good accuracy but also saves a lot of computational cost. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the decoupled method for time-dependent natural convection problem. For Part I, see [\textit{T. Zhang} et al., Numer. Methods Partial Differ. Equations 31, No. 6, 2135--2168 (2015; Zbl 1336.65172)].