Alternating direction implicit schemes based on SAV and IEQ approaches for nonlinear Allen-Cahn model

Invariant Energy Quadratization (IEQ) and Scalar Auxiliary Variable (SAV) methods are widely adopted for designing unconditionally energy-stable linear methods of phase field equations. This paper introduces and analyzes Alternative Direction Implicit (ADI) schemes, which are based on the IEQ and SAV frameworks, used for simulating the Allen-Cahn model. The proposed ADI-IEQ and ADI-SAV schemes retain the computational efficiency of the ADI method while reducing the overall complexity. We rigorously establish their energy stability and derive truncation error estimates, with both results holding under the same constraint on the stabilized coefficient within the discrete environment. Several numerical experiments are conducted to illustrate the convergence rates and the energy stability of the both schemes.