In this paper, we innovatively develop uniform/variable-time-step weighted and shifted BDF2 (WSBDF2) methods for the anisotropic Cahn-Hilliard (CH) model, combining the scalar auxiliary variable (SAV) approach with two types of stabilized techniques. Using the concept of $G$-stability, the uniform-time-step WSBDF2 method is theoretically proved to be energy-stable. Due to the inapplicability of the relevant G-stability properties, another technique is adopted in this work to demonstrate the energy stability of the variable-time-step WSBDF2 method. In addition, the two numerical schemes are all mass-conservative.Finally, numerous numerical simulations are presented to demonstrate the stability and accuracy of these schemes.

翻译：本文创新性地针对各向异性Cahn-Hilliard（CH）模型发展了均匀/可变时间步长的加权移位BDF2（WSBDF2）方法，将标量辅助变量（SAV）方法与两种稳定化技术相结合。利用$G$-稳定性的概念，理论上证明了均匀时间步长WSBDF2方法的能量稳定性。由于相关$G$-稳定性性质的不适用性，本文采用另一种技术来证明可变时间步长WSBDF2方法的能量稳定性。此外，两种数值格式均具有质量守恒性。最后，通过大量数值模拟验证了这些格式的稳定性和精度。