Abstract
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials.
Highlights
In recent years computer simulations are becoming an ever more important tool to study a large spectrum of physical problems, a trend supported by the increasing processor throughput and advances in the parallel computing research
The purpose of this work is to present a series of tools and methods which can be used to approach a wide range of problems and applications in porous media, characterised by different geometrical descriptions and involved in several transport phenomena and dynamics: from transport of dilute suspensions to heat transfer in porous structures
We have shown the computational challenges involved in the simulation of transport problems in the field of porous media or, more generally, in problems which feature multiple spatial scales, or whose evolution takes place over multiple temporal scales: examples of which we have
Summary
In recent years computer simulations are becoming an ever more important tool to study a large spectrum of physical problems, a trend supported by the increasing processor throughput and advances in the parallel computing research. While several promising open-source libraries and codes (Deal.II, UG, dune, GetFEM, just to cite a few) are available, there is still an urgent need of developing specific tools and workflow to approach particular classes of problems This is problematic in the case of very complex physics or inherently multi-scale problems such as heterogeneous media where, despite the current growing trend in non-physical data-driven science, computer modelling still remains the only practi-. The aim of this paper is to propose a fully open-source simulation workflow, show the validity and feasibility of a fully in-silico investigation, and introducing some specific novel methods and formulation to streamline the modelling and upscaling step We demonstrate this approach by solving three proof-of-concept problems. These are sometimes characterised by some ideal assumptions (e.g., geometrically simplified models, mostly linear and constant parameters, decoupled multi-physics), the tools presented in this work can be readily used for a number of important applications
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