Related papers: Upscaling multiphase flow through heterogeneous po…
An adaptive model for the description of flows in highly heterogeneous porous media is developed in~\cite{FP21,FP23}. There, depending on the magnitude of the fluid's velocity, the constitutive law linking velocity and pressure gradient is…
The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied. To this end, a rescaled zero-range…
When neglecting capillarity, two-phase incompressible flow in porous media is modelled as a scalar nonlinear hyperbolic conservation law. A change in the rock type results in a change of the flux function. Discretizing in one-dimensional…
The simulation of fluid flow in real, multiscale porous media remains challenging due to the complexity of nanoscale phenomena and the difficulty of developing upscaling methodologies. In this study, we introduce a multiscale filtration…
Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise…
In this study, we investigate the appeared complexity of two-phase flow (air-water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the time-dependent gas pressure. After obtaining of governing…
Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is often parameterized by a high-dimensional random variable. This…
In this paper, we propose a rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods [10]. Our proposed method consists of identifying multi-continua parameters via…
Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux-weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate…
The flow of non-Newtonian fluids is ubiquitous in many applications in the geological and industrial context. We focus here on yield stress fluids (YSF), i.e. a material that requires minimal stress to flow. We study numerically the flow of…
We propose a theory for erosional channelization induced by fluid flow in a saturated granular porous medium. When the local fluid flow-induced stress is larger than a critical threshold, grains are dislodged and carried away so that the…
In this paper we give a new proof of the homogenization result for an immiscible incompressible two-phase flow in double porosity media obtained earlier in the pioneer work by A. Bourgeat, S. Luckhaus, A. Mikeli\'c (1996) and in the paper…
Convection-driven porous media flows are common in industrial processes and in nature. The multiscale and multiphase character of these systems and the inherent non-linear flow dynamics make convection in porous media a complex phenomenon.…
We analyze the mixing, migration and spreading of a gravity current in a heterogeneous porous medium using high-fidelity numerical simulations. Heterogeneity is represented by log-normal permeability fields of varying correlation lengths…
Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous medium---but not in bulk solution. The reason…
In this study, we investigate the appeared complexity of two-phase flow (air/water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the timedependent gas pressure. After obtaining of governing…
Over the last few decades, phase-field equations have found increasing applicability in a wide range of mathematical-scientific fields (e.g. geometric PDEs and mean curvature flow, materials science for the study of phase transitions) but…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open…
A new computational framework for the simulation of turbulent flow through complex objects and along irregular boundaries is presented. This is motivated by the application of metal foams in compact heat-transfer devices, or as catalyst…