The Phase Field Method stands as a promising technique for modeling complex two-phase and multi-phase flow systems, with the advective Cahn–Hilliard equation adept at capturing the evolution of intricate interfacial structures. However, achieving simulation accuracy necessitates the preservation of the diffuse interface profile, which is often challenged by the convection term within the Cahn–Hilliard equation, leading to deviations from the equilibrium interface state. To address this challenge, we introduce an innovative approach aimed at iteratively restoring the equilibrium interface profile after each time step. This method combines a level-set profile-corrected equation with an algebraic relation between the phase field and the signed distance function, resulting in a preservation equation that relies on the phase-field-related signed distance function rather than the phase field function itself. Quantitative computational tests affirm the effectiveness of this approach in minimizing discretization errors, reducing dependence on the numerical Pclet number, and improving mass conservation accuracy for each phase, all while reducing computational time by approximately 20-fold due to the coarser grid used. Validation through simulations across various scenarios demonstrates the approach’s reliability, with results closely aligning with analytical solutions, prior numerical findings, and experimental data, thereby underscoring the efficiency and precision of our proposed approach.

中文翻译：

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不可压缩两相流相场建模的界面轮廓保持方法

相场法是一种有前景的复杂两相流和多相流系统建模技术，平流 Cahn-Hilliard 方程擅长捕捉复杂界面结构的演化。然而，要实现模拟精度，就必须保留扩散界面轮廓，这通常会受到 Cahn-Hilliard 方程中对流项的挑战，导致偏离平衡界面状态。为了应对这一挑战，我们引入了一种创新方法，旨在在每个时间步骤后迭代恢复平衡界面轮廓。该方法将水平集轮廓校正方程与相场和有符号距离函数之间的代数关系相结合，产生依赖于与相场相关的有符号距离函数而不是相场函数本身的保存方程。定量计算测试证实了该方法在最小化离散化误差、减少对数值 Pclet 数的依赖性以及提高每个相的质量守恒精度方面的有效性，同时由于使用了较粗糙的网格，因此将计算时间减少了约 20 倍。通过各种场景的模拟验证证明了该方法的可靠性，结果与解析解、先前的数值结果和实验数据密切相关，从而强调了我们提出的方法的效率和精度。