On the use of the consistent splitting scheme for double-diffusive convection flows in mixed finite element formulations

Abstract

This paper describes the so-called consistent splitting scheme (CSS) for solving unsteady double-diffusive convection (DDC) problems using the mixed finite element method. The CSS was chosen to numerically solve the primitive form of the unsteady governing equations for decoupling the velocity variables and the pressure. Both first- and second-order accurate temporal and spatial approximations have been implemented for unsteady DDC problems. The results obtained with the described numerical methods compare favourably with the existing numerical result.

Keywords:

• Mixed finite element
• Consistent splitting scheme
• Double-diffusive convection

Acknowledgements

The author thanks the referees for their valuable comments and suggestions. He would like to acknowledge the encouragement and helpful suggestions from Professor Jun Zou and to express his appreciation to Frank Ng for help with the computing facility. The computations were performed on the IBM RS/6000 SP system at the Chinese University of Hong Kong. Last but not least, the author is grateful beyond all exponential orders to Anita Spence who read his earlier manuscript.

Notes

^†In Boussinesq approximation, the density is assumed to be constant except in the buoyancy term of temperature and concentration of momentum equation [cf. equation (1)].

Additional information

Notes on contributors

J. C.-F. Wong

Email: [email protected]