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.

中文翻译：

---

基于 Boussinesq 系统标量辅助变量 (SAV) 方法的完全解耦数值格式的误差估计


在本文中，我们将研究 Boussinesq 方程完全解耦数值格式的无条件稳定性和误差估计。新构造的数值格式基于压力修正技术和SAV方法，其中所有耦合项和非线性项完全解耦，即只需要求解几个线性常系数方程。我们严格证明了时间推进方案的无条件稳定性和收敛性，并讨论了算法实现的所有细节。最后，我们进行了一些数值实验来验证其稳定性和准确性。