We propose and analyze two novel decoupled numerical schemes for solving the Cahn-HilliardStokes-Darcy (CHSD) model for two-phase flows in karstic geometry. In the first numerical scheme, we explore a fractional step method (operator splitting) to decouple the phase-field (Cahn-Hilliard equation) from the velocity field (Stokes-Darcy fluid equations). To further decouple the Stokes-Darcy system...

The problem of hydrodynamic dispersion in non-Darcy free convection heat and mass transfer from vertical surface embedded in a porous medium has been presented. The Forchheimer extension is considered in the flow equations. The flow, temperature and concentration fields in Darcy and non-Darcy porous media are observed to be governed by complex interactions among the diffusion rate Le, buoyancy ...

Numerical simulation of uid ow in a hydrocarbon reservoir has to ac count for the presence of wells The pressure of a grid cell containing a well is di erent from the average pressure in that cell and di erent from the bottomhole pressure for the well Peaceman This paper presents a study of grid pressures obtained from the simulation of single phase ow through an isotropic porous medium using d...

The Darcy model is based on a plethora of assumptions. One of the most important assumptions is that the Darcy model assumes the drag coefficient to be constant. However, there is irrefutable experimental evidence that viscosities of organic liquids and carbon-dioxide depend on the pressure. Experiments have also shown that the drag varies nonlinearly with respect to the velocity at high flow r...

Abstract. Consider an incompressible fluid in a region Ωf flowing both ways across an interface, I, into a porous media domain Ωp saturated with the same fluid. The physical processes in each domain have been well studied and are described by the Stokes equations in the fluid region and the Darcy equations in the porous media region. Taking the interfacial conditions into account produces a sys...

The flow past an impermeable sphere embedded in a fluid saturated porous medium was studied numerically considering valid the Brinkman−Forchheimer−Darcy (or Brinkman−Hazen−Dupuit−Darcy) model. The flow is viscous, laminar, axisymmetric, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function vorticity equations were solved numerically in spherical c...

We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, i...

In this paper we investigate the accuracy of a Darcy-scale model for competitive adsorption in a porous medium through comparison with a smoothed particle hydrodynamics (SPH) pore-scale model. SPH is a Lagrangian, particle based modeling method which uses the particles as interpolation points to directly discretize the governing equations of the system. The models consider a binary system of co...

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...

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...