A Fundamental Assessment of Computational Porosity
Creators: name: Kalderon, Moris
Publisher: name: Zenodo
Year: 2017
Subjects: granular materials
Discrete Element Method
homogenization
coarse graining

description: One challenge of today’s research is the realistic simulation of granular materials consisting of millions of particles. Coupled DEM-CFD models are becoming all the more attractive as computers are gaining computational power and complex simulations are becoming feasible. In geotechnical engineering coupled analyses can lead towards the understanding of internal erosion in Damns, liquefaction of sands and of other compound phenomena where fluid flow takes place.<br> One of the most crucial steps of the coupled algorithm is the porosity computation at every region of the model’s domain. Thus, the establishment of an efficient and accurate way of calculating porosity has become the area of study of many researchers. Many different approaches have been proposed during the last years and the majority of them is based on binning and calculating porosity on a number of predefined fluid-cells. The prevailing binning methods are the Particle Centroid Method (PCM), which is a quite crude but easy-to-implement method, the exact methods that deal with particle’s geometry, and approximate methods that “sacrifice” accuracy to reduce the computational cost. Other methods are based on statistical distributions and diffusion (“smearing” methods), while recently more implicit methods are proposed that are not extensively tested.<br> In this dissertation the main methods that have been used in literature are assessed and are used as a reference to program modified versions that obey to similar rules and logic but approach porosity calculation differently. Furthermore, two extra methods are proposed as alternatives to the commonly used coarse-graining methods; Pixel and Hybrid method which are suitable for both two and three dimensional simulations. The pixel method adopts a logic similar to that of pixels to discretize and calculate the domain occupied by particles at every fluid-cell and the Hybrid method that uses analytical calculations, when is feasible and easy to implement, and pixels at the “difficult” regions, reducing by this way the computational cost of Pixel method. These methods are examined compared to the other proposed methods; the simple method (equivalent to Particle Centroid Method), which constitutes the lower boundary in terms of precision, the analytical method that is developed based on mathematical formulas and integrations for the calculation of the particles’ fractions and two “smearing” methods, the Statistical distribution based method and the Diffusion based method.<br> It is shown that the PCM is relatively accurate for 2D simulations, while in three-dimensions the error is much higher and should be avoided. The proposed Analytical method proved very efficient in both two and three dimensions and is used as a reference concerning the accuracy of the other methods. The smearing methods present a much higher accuracy compared to the PCM, especially in three-dimensions, but a further study is proposed for their assessment. The proposed Pixel method can yield high accuracy in two dimensions but is considered as computationally expensive in three dimensions. On the other hand, the Hybrid method preserves Pixels method’s advantages, while reduces the computational cost and increases efficiency in three dimensions.<br> Finally, the Analytical method is used for porosity calculation of two and three dimensional samples in order to investigate the factors that affect porosity in granular soils.