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

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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.