Subgrid Scale Modeling and Efficient Finite Element Simulation of Fiber Suspension Flows

该项目的目标是开发用于造纸和回收的纤维悬浮流动的多尺度建模框架和数值模拟技术。二阶方向张量的演化方程将为其四阶对应物配备一个新的基于反卷积的闭包。提出的亚网格尺度建模方法涉及通过求解正则化逆问题重建光纤取向概率密度函数。为了避免非物理取向状态和执行离散最大原则，将定制的通量限制技术纳入有限元离散化。采用自适应拉格朗日模型模拟光纤在近壁区的流动。通过边界层内缘的透射条件实现与欧拉模型的耦合。动量通量将使用类似于不连续伽辽金方法来定义，而拉格朗日纤维的边界条件将从局部取向状态和体积分数来推断。本文将特别关注耦合问题的高效迭代求解器的设计，该求解器基于软件包FEATFLOW及其扩展，可用于分散两相流。所提出的多尺度域分解方法的每个组成部分将通过具有代表性的基准问题的数值研究或由工业合作伙伴福伊特纸业有限公司提供的实验数据进行验证。

The goal of this project is the development of a multiscale modeling framework and numerical simulation techniques for fiber suspension flows with applications to papermaking and recycling. The evolution equation for the 2nd-order orientation tensor will be equipped with a novel deconvolution-based closure for its 4th-order counterpart. The proposed approach to subgrid scale modeling involves reconstruction of a fiber orientation probability density function by solving a regularized inverse problem. To avoid nonphysical orientation states and enforce the discrete maximum principle, custom-made flux limiting techniques will be incorporated into the finite element discretization. The flow of fibers in the near-wall region will be simulated using an adaptive Lagrangian model. The coupling with the Eulerian model for the bulk flow will be realized via transmission conditions at the inner edge of the boundary layer. The momentum fluxes will be defined using an analogy to discontinuous Galerkin methods, whereas the boundary conditions for Lagrangian fibers will be inferred from the local orientation state and volume fraction. Special attention will be paid to the design of efficient iterative solvers for the coupled problem on the basis of the software package FEATFLOW and its extensions to disperse two-phase flows. Each component of the proposed multiscale domain decomposition method will be validated using numerical studies for representative benchmark problems or experimental data provided by the industrial partner Voith Paper GmbH.