Error estimate of a fully decoupled numerical scheme based on the Scalar Auxiliary Variable (SAV) method for the Boussinesq system

In this paper, we will investigate the unconditional stability and error estimate of the fully decoupled numerical scheme for the Boussinesq equations. The newly constructed numerical scheme is based on the pressure correction technique and the SAV method, in which all coupling terms and nonlinear terms are completely decoupled, that is, we only need to solve several linear constant -coefficient equations. We rigorously prove the unconditional stability and convergence of the time -marching scheme and discuss all the details of the algorithm implementation. Finally, we implement some numerical experiments to verify its stability and accuracy.