Variable-order time-fractional diffusion equations (VO-tFDEs), which can be used to model solute transport in heterogeneous porous media are considered. Concerning the well-posedness and regularity theory (cf., Zheng & Wang, Anal. Appl., 2020), two finite difference ADI and compact ADI schemes are respectively proposed for the two-dimensional VO-tFDE. We show that the two schemes are unconditionally stable and convergent with second and fourth orders in space with respect to corresponding discrete norms. Besides, efficiency and practical computation of the ADI schemes are also discussed. Furthermore, the ADI and compact ADI methods are extended to model three-dimensional VO-tFDE, and unconditional stability and convergence are also proved. Finally, several numerical examples are given to validate the theoretical analysis and show efficiency of the ADI methods.

变阶时间分数扩散方程 (VO-tFDE) 可用于模拟非均质多孔介质中的溶质输运。关于适定性和正则性理论 (cf., Zheng & Wang, Anal. Appl., 2020)，分别为二维 VO-tFDE 提出了两种有限差分 ADI 和紧凑 ADI 方案。我们表明这两种方案是无条件稳定的，并且相对于相应的离散范数在空间中具有二阶和四阶收敛。此外，还讨论了 ADI 方案的效率和实际计算。此外，将 ADI 和紧凑 ADI 方法扩展到三维 VO-tFDE 建模，并证明了无条件稳定性和收敛性。最后，