The Earth’s mantle (or, e.g., a glacier) involves a deformable solid matrix phase within which a second phase, a fluid, may form due to melting processes. The system is modeled as a dual-continuum mixture, with at each point of space the solid matrix being governed by a Stokes flow and the fluid melt, if it exists, being governed by Darcy’s law. This system is mathematically degenerate when the...

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...

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 ...

We present an overview of a modern, efficient approach for uncoupling groundwater–surface water flows governed by the fully evolutionary Stokes–Darcy equations. Referred to as non-iterative partitioned methods, these algorithms treat the coupling terms explicitly and at each time level require only one Stokes and one Darcy sub-physics solve, thus taking advantage of existing solvers optimized f...

This paper presents a new stabilized finite element method for the Darcy–Stokes equations also known as the Brinkman model of lubrication theory. These equations also govern the flow of incompressible viscous fluids through permeable media. The proposed method arises from a decomposition of the velocity field into coarse/resolved scales and fine/unresolved scales. Modelling of the unresolved sc...

We study two novel decoupled energy-law preserving numerical schemes for solving the CahnHilliard-Darcy (CHD) system which models two-phase flow in porous medium or in a Hele-Shaw cell. In the first scheme, the velocity in the Cahn-Hilliard equation is treated explicitly so that the Darcy equation is completely decoupled from the Cahn-Hilliard equation. In the second scheme, an intermediate vel...

Flow in porous Silicon Carbide (SiC) has been investigated in order to increase the understanding of the determining parameters. Porous SiC is used in the fabrication of ceramic membranes, for use in cross-flow and dead-end filtration. Therefore, a description of the flow would help to design more efficient filtration modules, and to improve the use of the existing modules. The investigation pe...

This paper focuses on the acceleration of Schwarz method by Aitken’s convergence technique considering special structure Schwarz’s error operator between two consecutive iterates domain decomposition’s interfaces. The new proposed method, called Sparse Aitken-Schwarz builds a low-rank space for each subdomain to approximate true solution its interfaces instead building associated gathered subdo...

Flow and transport in fractured porous media are of paramount importance for many applications such as petroleum exploration and production, geological storage of carbon dioxide, hydrogeology, or geothermal energy. We consider here the two-phase discrete fracture model introduced in [3] which represents explicitly the fractures as codimension one surfaces immersed in the surrounding matrix doma...