标题： 裂缝和薄非均质性作为罗宾-温特塞尔界面条件 显示英文标题

标题： Fractures and thin heterogeneities as Robin-Wentzell interface conditions

摘要： 我们正式推导了用于模拟达西流问题中裂缝的界面条件，以及更一般地，用于表达为通量散度的异质扩散问题中的细长包含物。 通过在包含物内对控制方程进行形式积分，我们确定得到的界面条件对于通量跳跃是温特塞尔类型，对于通量平均是罗宾类型。 值得注意的是，通量跳跃条件是非传统的，涉及对界面两侧解的平均值应用切向扩散算子。 引入了相应的弱形式，提供了一个易于应用于有限元离散化的框架。 广泛的数值验证突显了所提出建模技术的鲁棒性和通用性。 结果表明，该方法在适应各种材料特性、管理包含物网络以及自然处理不同孔隙度的裂缝方面非常有效——而无需显式表示裂缝的几何形状。 显示英文摘要

摘要： We formally derive interface conditions for modeling fractures in Darcy flow problems and, more generally, thin inclusions in heterogeneous diffusion problems expressed as the divergence of a flux. Through a formal integration of the governing equations within the inclusions, we establish that the resulting interface conditions are of Wentzell type for the flux jump and Robin type for the flux average. Notably, the flux jump condition is unconventional, involving a tangential diffusion operator applied to the average of the solution across the interface. The corresponding weak formulation is introduced, offering a framework that is readily applicable to finite element discretizations. Extensive numerical validation highlights the robustness and versatility of the proposed modeling technique. The results demonstrate its effectiveness in accommodating a wide range of material properties, managing networks of inclusions, and naturally handling fractures with varying apertures -- all without requiring an explicit geometric representation of the fractures.