Two Improved Stabilized Generalized Scalar Auxiliary Variable (isGSAV) Schemes Preserving Energy Dissipation Law and Maximum Bound Principle for Gradient Flows

In this paper, we propose two improved stabilized generalized scalar auxiliary variable (isGSAV) methods for general gradient flows. Firstly, we reformulate the phase‐field variable and chemical potential via an auxiliary variable to enhance numerical accuracy and consistency. A stabilization term is added to improve the stability of the intermediate variable . Theoretical analysis proves that the proposed schemes preserve the energy dissipation law and maximum bound principle for Allen‐Cahn type equations. Secondly, we rearrange the conventional solution sequence of unknowns, allowing direct updates of numerical solutions through a single linear system. This refinement significantly improves the accuracy and efficiency of simulations, and relaxes the constraint on the constant associated with the lower bound of the total free energy. The proposed methods inherit all advantages of the standard GSAV method and yield high‐order unconditionally stable schemes for general gradient flows. Finally, extensive numerical experiments and comparisons are performed to validate the effectiveness of the proposed methods.