We aim at proposing novel stable finite element methods for the mixed Darcy equation with heterogeneous coefficients within a space splitting framework. We start from the primal hybrid formulation of the elliptic model for the pressure. Localization of this infinite-dimensional problem leads to element-level boundary value problems which embed multiscale and high-contrast features in a natural ...

The study of non-equilibrium thermal convection in an anisotropic porous layer saturated with a visco-elastic fluid is carried out to find how the anisotropy and temperature affect onset convection. small perturbation method applied obtain linearized form equations are then solved by using normal mode technique. viscoelasticity considered taking Oldrovd-B momentum equation two separate expressi...

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The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linea...

This paper investigates the influence of the effect of viscous dissipation and radiation on natural convection heat transfer from vertical flat plate in a non-Darcy porous media saturated with non-Newtonian fluid of variable viscosity. The wall and the ambient medium are maintained at constant but different levels of temperature. The Ostwald–de Waele power law model is used to characterize the ...

Steam injection is the most suitable of Enhanced Oil Recovery (EOR) methods to recover high viscosity oil. This is due to the capabilities of steam to reduce oil viscosity and increase the sweep capability of oil from the injection well toward the production well. Oil operating conditions in production should be match well with the operating condition target at the bottom of the production well...

Based on the production data and statistical information of a practical oilfield, it is proved that the flow rule in wormhole or extra wormhole can be regarded as a high speed Non-Darcy flow, and used the Forchheimer equation to represent. The Forchheimer model is superior to the exponent model and Mazaheri model. Then, the productivity equation of poorly consolidated reservoir with wormhole is...

A new multiscale method combined with model order reduction is proposed for flow problems in three-scale porous media. We derive an effective three-scale model that couples a macroscopic Darcy equation, a mesoscopic Stokes-Brinkman equation, and a microscopic Stokes equation. A corresponding three-scale numerical method is then derived using the finite element discretization with numerical quad...

We consider a diffuse interface model for tumor growth recently proposed in [3]. In this new approach sharp interfaces are replaced by narrow transition layers arising due to adhesive forces among the cell species. Hence, a continuum thermodynamically consistent model is introduced. The resulting PDE system couples four different types of equations: a Cahn-Hilliard type equation for the tumor c...