Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model

In this work, we develop a novel Lagrangian model able to predict solute mixing in heterogeneous porous media. The Spatial Markov model has previously been used to predict effective mean conservative transport in flows through heterogeneous porous media. In predicting effective measures of mixing on larger scales, knowledge of only the mean transport is insufficient. Mixing is a small scale process driven by diffusion and the deformation of a plume by a non-uniform flow. In order to capture these small scale processes that are associated with mixing, the upscaled Spatial Markov model must be extended in such a way that it can adequately represent fluctuations in concentration. To address this problem, we develop downscaling procedures within the upscaled model to predict measures of mixing and dilution of a solute moving through an idealized heterogeneous porous medium. The upscaled model results are compared to measurements from a fully resolved simulation and found to be in good agreement.

Fully resolved numerical simulations of fused deposition modeling. Part I: fluid flow

Purpose This paper aims to present a first step toward developing a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling (FDM). Design/methodology/approach A front-tracking/finite volume method previously developed for simulations of multiphase flows is extended to model the injection of hot polymer and its cooling down. Findings The accuracy and convergence properties of the new method are tested by grid refinement, and the method is shown to produce convergent solutions for the shape of the filament, the temperature distribution, contact area and reheat region when new filaments are deposited on top of previously laid down filaments. Research limitations/implications The present paper focuses on modeling the fluid flow and the cooling. The modeling of solidification, volume changes and residual stresses will be described in Part II. Practical implications The ability to carry out fully resolved numerical simulations of the fusion deposition process is expected to help explore new deposition strategies and provide the “ground truth” for the development of reduced-order models. Originality/value The present paper is the first fully resolved simulation of the deposition in fusion filament modeling.