Error Analysis of BDF2 Scheme for the Boussinesq System Based on Exponential Scalar Auxiliary Variable

Abstract A linear BDF2 numerical scheme is proposed to solve the Boussinesq system. By using the exponential scalar auxiliary variable (E-SAV) approach, we explicitly deal with the nonlinear terms of the Boussinesq system, and decouple the velocity and temperature in the numerical simulation. These numerical scheme is unconditionally stable. We give rigorous error analysis for the velocity and temperature. Numerical experiment is performed to verify the proposed numerical scheme.