基于Onsager原理的任意域热力学一致Cahn-Hilliard模型区域嵌入方法
Onsager Principle-Based Domain Embedding for Thermodynamically Consistent Cahn-Hilliard Model in Arbitrary Domain
AI总结：
本文提出基于Onsager原理的区域嵌入（OPBDE）方法，将任意域Cahn-Hilliard模型扩展至规则域，确保热力学一致性，并通过渐近分析和保结构数值格式验证了其准确性与处理任意几何梯度流问题的能力。
摘要：
具有两个给定边界条件的任意域原始Cahn-Hilliard模型被扩展为更大规则域上具有齐次Neumann边界条件的Cahn-Hilliard型模型。该扩展基于Onsager原理的区域嵌入（OPBDE）方法，该方法作为一种系统性区域嵌入框架被开发，以确保热力学一致性。通过引入修正的守恒律，原始区域边界处的通量被作为源项纳入守恒律。我们的变分方法表明，即使没有关于泵入系统的自由能速率具体形式的先验知识，Onsager原理仍然是推导扩展系统本构方程的有效工具。该方法从自由能及其耗散的角度阐明了扩展模型的内在结构。对扩展的OPBDE Cahn-Hilliard模型进行了渐近分析，证明原始Cahn-Hilliard模型（包括其边界条件）可以被完全恢复。为了验证我们的方法，开发了一种保结构数值格式来离散化扩展模型。数值结果表明，OPBDE Cahn-Hilliard模型准确、有效且稳健，突出了OPBDE方法处理任意区域几何中梯度流问题的能力。
英文摘要：
The original Cahn-Hilliard model in an arbitrary domain with two prescribed boundary conditions is extended to a Cahn-Hilliard-type model in a larger, regular domain with homogeneous Neumann boundary conditions. The extension is based on the Onsager principle-based domain embedding (OPBDE) method, which has been developed as a systematic domain embedding framework to ensure thermodynamic consistency. By introducing a modified conservation law, the flux at the boundary of the original domain is incorporated into the conservation law as a source term. Our variational approach demonstrates that, even without a prior knowledge on the specific form of the rate of free energy pumped into the system, the Onsager principle remains an effective instrument in deriving the constitutive equation of the extended system. This approach clarifies the intrinsic structure of the extended model in the perspectives of free energy and its dissipation. Asymptotic analysis is carried out for the extended OPBDE Cahn-Hilliard model, demonstrating that the original Cahn-Hilliard model, including its boundary conditions, can be fully recovered. To validate our approach, a structure-preserving numerical scheme is developed to discretize the extended model. Numerical results show that the OPBDE Cahn-Hilliard model is accurate, effective, and robust, highlighting the capability of the OPBDE method in handling gradient flow problems in arbitrary domain geometries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
