Scalar auxiliary variable pressure-correction method for natural convection problems⋆

Abstract

In this article, we present first-order standard pressure-correction and second-order rotational pressure-correction algorithms using an exponential scalar auxiliary variable (SAV) approach for the natural convection problems. The SAV pressure-correction method is linear and decoupled with explicit treatment of nonlinear terms, so it only needs to solve a sequence of Poisson equations for velocity and pressure at each time step. Furthermore, we proved the first- and second-order algorithms are unconditionally stable and established error estimates of the velocity, temperature and pressure approximation for the first-order algorithms without any restriction on the time step. Finally, some numerical experiments are provided to support the theoretical analysis and to show the performances of our proposed algorithms.

Keywords:

• Natural convection problems
• Scalar auxiliary variable
• Pressure-correction
• Stability analysis
• Error estimates

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the authors.