耦合Stokes-Brinkman-Darcy流动的硬迹一阶残差学习
Hard-Trace First-Order Residual Learning for Coupled Stokes-Brinkman-Darcy Flow
- School of Mathematics, Shandong University（山东大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
针对耦合Stokes-Brinkman-Darcy流动，提出一种混合一阶硬迹残差学习方法，通过共享迹和压力校正实现高精度求解，误差低至0.87%。
中文摘要 AI 辅助
Stokes-Brinkman-Darcy（SBD）模型通过有限厚度的Brinkman层将自由流动与多孔流动连接起来。所提出的求解这些耦合方程的方法包括混合一阶形式、共享界面迹和硬牵引约束，以及基于边界质量平衡的压力校正。独立的应力、Darcy通量和压力梯度辅助量避免了网络输出的二阶导数。边界提升和共享迹精确施加外部和界面运动学条件，而应力映射强制执行本征Brinkman-Darcy力平衡。训练后，通过积分动量关系确定压力校正，无需参考压力标签。在两个制造解和三种渗透率下，校正后的平均上压力相对$L^2$误差范围为0.87%至2.58%；校正每次运行均降低了上压力$L^2$误差和完整Brinkman压力$H^1$误差。配对对照实验评估了界面共享和牵引执行的贡献。一个非制造过滤问题测试了混合边界适应性，与独立细化的有限元参考进行比较，所有四次运行均满足规定的场和物理一致性标准。
英文摘要
Stokes-Brinkman-Darcy (SBD) models connect free flow and porous flow through a Brinkman layer of finite thickness. The proposed method for solving these coupled equations consists of a mixed first-order formulation, shared interface traces and hard traction constraints, and a pressure correction based on boundary mass balance. Independent stresses, Darcy flux and pressure-gradient auxiliaries avoid second derivatives of network outputs. Boundary liftings and shared traces impose exterior and interface kinematic conditions exactly, while a stress map enforces native Brinkman-Darcy force balance. An integral momentum relation determines the pressure correction after training, without reference-pressure labels. Across two manufactured solutions and three permeabilities, mean corrected upper-pressure relative $L^2$ errors range from 0.87% to 2.58%; correction reduces both upper-pressure $L^2$ errors and the full Brinkman-pressure $H^1$ error in every run. Paired controls assess the contributions of interface sharing and traction enforcement. A non-manufactured filtration problem tests mixed-boundary adaptation against an independently refined finite-element reference, with all four runs satisfying the prescribed field and physical-consistency criteria.
