A novel pressure-correction projection finite element method for incompressible natural convection problem with variable density

Abstract

This work introduces a novel pressure-correction (PC) projection finite element method for solving the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods. We choose the conforming finite element pair to approximate the density, the velocity, the pressure, and the temperature field, respectively. Moreover, the stability analysis of the first-order PC projection finite element method is given. Finally, ample numerical results are presented to demonstrate the efficacy and accuracy of the proposed method.

Acknowledgments

The authors would like to thank the editor and referees for their valuable comments and suggestions which helped us to improve the results of this paper.

Additional information

Funding

This work was in parts supported by the Research Fund from Key Laboratory of Xinjiang Province (No. 2017D04030), the NSF of China (No. 11671345), and the High-Level Personal Foundation of Henan University of Technology (No. 2017BS028).