Darcy-scale models of flow and transport in porous media often fail to describe experimentally observed phenomena, while their pore-scale counterparts are accurate but can be computationally prohibitive. Most numerical multiscale models, which seek to combine these two descriptions, require empirical closures and/or assumptions about the behavior of pore-scale quantities at the continuum (Darcy...

We investigate the discretization of Darcy flow through fractured porous media on general polyhedral meshes. We consider a hybrid dimensional model, invoking a complex network of planar fractures. The model accounts for matrix-fracture interactions and fractures acting either as drains or as barriers, i.e. we have to deal with pressure discontinuities at matrix-fracture interfaces. The numerica...

We derive a Cahn–Hilliard–Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a coupling of the Cahn–Hilliard–Darcy equations to a system of reaction-diffusion equations a multitude of phenomena such as nutrient diffusion and consumption, angi...

We study the validity of the quasistatic approximation in the fully evolutionary Stokes-Darcy problem for the coupling of groundwater and surface water flows, as well as the dependence of the problem on the specific storage parameter. In the coupled equations that describe the groundwater and surface water flows for an incompressible fluid, the specific storage, S0, represents the volume of wat...

Forced convection in a tube with its core partially filled with a porous medium is treated both analytically and numerically to find its high heat transfer performance. Assuming a fully developed flow subject to a constant heat flux, both friction factor and Nusselt number are presented explicitly as functions of the Reynolds number, Darcy number and porous core diameter ratio. Partial filling ...

The quadratic and power laws are two typical formulations that can be used to extend the Darcy law to non-Darcy flows through porous media. Both laws are reformulated in the dimensionless form in this study. They are then evaluated by fitting to experimental data with specified variations in seepage velocity, which were specifically collected for a simplified ordered porous model. The results s...

Convection in a partitioned porous layer is considered where the thin partition causes a mechanical isolation of the two identical sublayers from one another, but heat may neveretheless conduct freely. An unsteady solver that employs the multigrid method is employed to determine steady-state strongly nonlinear for values of the Darcy–Rayleigh number up to eight times its critical value. The pre...

Natural convection in a square enclosure having two wavy vertical walls is studied. An enclosure is filled with fluid-saturated porous media. A cavity is heated spatially on bottom wall while remaining walls are maintained at lower temperature. The objective of this study is to examine the flow field, temperature distribution and heat transfer inside the cavity when values of Darcy number, Rayl...

Understanding and controlling fluids flow at the microscale is a matter of growing scientific and technological interest. Flow enhancements of water-based nanoparticle dispersions through microscale porous media are investigated through twelve hydrophilic sedimentary rocks with pore-throat radius between 1.2 and 10 μm, which are quantitatively explained with a simple model with slip length corr...

In this paper, we first present the THex algorithm that refines a tetrahedral mesh into a hexahedral mesh. Strategies for efficient implementation of the THex algorithm are discussed. Then we present the lowest order weak Galerkin (WG) (Q0, Q0;RT[0]) finite element method for solving the Darcy equation on general hexahedral meshes. This simple solver uses constant pressure unknowns inside hexah...