We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a special case of a previously derived and studied system of equations which describes phase separation in ternary mixtures. We prove the scheme is both energy stable and respects the analytical bounds of the solution. Furthermore, we present numerical demonstrations of the theoretical results using both the Flory-Huggins (FH) and Ginzburg-Landau (GL) free-energy potentials.

翻译：我们针对非局部Cahn-Hilliard方程提出了一种基于有限体积的数值格式，该格式融合了近期梯度流方程与非局部Cahn-Hilliard方程数值格式的设计思想。所研究的方程是此前推导并分析的三元混合物相分离方程系统的一个特例。我们证明了该格式满足能量稳定性，并能保持解的解析有界性。此外，我们分别采用Flory-Huggins (FH)和Ginzburg-Landau (GL)自由能势能进行了数值实验，验证了理论结果。