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.