In this work we introduce novel numerical schemes for a penalized version of the ternary Cahn-Hilliard system for the purpose of creating accurate and efficient numerical schemes of interfacial dynamics with three components as well as some results extending these ideas to systems with four or more components. The first scheme is linear, decoupled, first order accurate, and unconditionally energy stable. Next, we present a second scheme which is a conditionally energy stable modification of the first scheme, but has greatly reduced computational cost. Finally, we present a third scheme which is linear and second order accurate but the unknowns are coupled. Moreover, we present several numerical simulations in two and three dimensions to give a comprehensive overview of each scheme and the cost-benefit analysis associated with designing a method for energy-stability, efficiency, and accuracy.

翻译：本文针对惩罚型三元Cahn-Hilliard系统提出新型数值格式，旨在构建精确高效的三组分界面动力学数值方法，并将相关思想拓展至四组分及以上系统。首个格式为线性解耦的一阶精度格式，具有无条件能量稳定性。其次提出第二种格式，作为首格式的条件性能量稳定改进版本，其计算成本显著降低。最后提出第三种线性二阶精度格式，但未知量呈耦合形式。此外，我们通过二维与三维数值模拟全面评估各格式性能，并就能量稳定性、计算效率与精度之间的权衡关系进行成本效益分析。