Title: Intelligent backpropagated neural networks application on Couette-Poiseuille flow of variable viscosity in a composite porous channel filled with an anisotropic porous layer Show Chinese title

Title: 智能反向传播神经网络在复合多孔通道中变粘度库埃特-泊肃叶流中的应用

Abstract: This study examines Couette-Poiseuille flow of variable viscosity within a channel that is partially filled with a porous medium. To enhance its practical relevance, we assume that the porous medium is anisotropic with permeability varying in all directions, making it a positive semidefinite matrix in the momentum equation. We assume the Navier-Stokes equations govern the flow in the free flow region, while the Brinkman-Forchheimer-extended Darcy's equation governs the flow inside the porous medium. The coupled system contains a nonlinear term from the Brinkman-Forchheimer equation. We propose an approximate solution using an iterative method valid for a wide range of porous media parameter values. For both high and low values of the Darcy number, the asymptotic solutions derived from the regular perturbation method and matched asymptotic expansion show good agreement with the numerical results. However, these methods are not effective in the intermediate range. To address this, we employ the artificial Levenberg-Marquardt method with a back-propagated neural network (ALMM-BNN) paradigm to predict the solution in the intermediate range. While it may not provide the exact solutions, it successfully captures the overall trend and demonstrates good qualitative agreement with the numerical results. This highlights the potential of the ALMM-BNN paradigm as a robust predictive tool in challenging parameter ranges where numerical solutions are either difficult to obtain or computationally expensive. The current model provides valuable insights into the shear stress distribution of arterial blood flow, taking into account the variable viscosity of the blood in the presence of inertial effects. It also offers a framework for creating glycocalyx scaffolding and other microfluidic systems that can mimic the biological glycocalyx. Show Chinese abstract

Abstract: 本研究考察了在部分填充多孔介质的通道中可变粘度的Couette-Poiseuille流动。 为了增强其实际相关性，我们假设多孔介质是各向异性的，渗透率在所有方向上变化，使其在动量方程中成为半正定矩阵。 我们假设Navier-Stokes方程支配自由流动区域的流动，而Brinkman-Forchheimer扩展的Darcy方程支配多孔介质内的流动。 耦合系统包含来自Brinkman-Forchheimer方程的非线性项。 我们提出了一种近似解，该解适用于广泛的多孔介质参数值。 对于Darcy数的高值和低值，从常规摄动方法和匹配渐近展开中得到的渐近解与数值结果有很好的一致性。 然而，这些方法在中间范围内效果不佳。 为了解决这个问题，我们采用人工Levenberg-Marquardt方法与反向传播神经网络（ALMM-BNN）范式来预测中间范围内的解。 虽然它可能无法提供精确解，但它成功捕捉了整体趋势，并与数值结果表现出良好的定性一致性。 这突显了ALMM-BNN范式在数值解难以获得或计算成本高昂的挑战性参数范围中的强大预测潜力。 当前模型为考虑惯性效应下血液的剪切应力分布提供了有价值的见解。 它还为创建糖萼支架和其他可以模拟生物糖萼的微流控系统提供了一个框架。