Numerical Analysis of a Second-Order Algorithm for the Time-Dependent Natural Convection Problem

In this paper, a second-order algorithm based on the spectral deferred correction method is constructed for the time-dependent natural convection problem, which allows one to automatically increase the accuracy of a first-order backward-Euler time-stepping method through using spectral integration on Gaussian quadrature nodes and constructing the corrections. A complete theoretical analysis is presented to prove that this algorithm is unconditionally stable and possesses second-order accuracy in time. Numerical examples are given to confirm the theoretical analysis and the effectiveness of our algorithm.