In this article, we present two Monte Carlo methods to solve some problems related to the Darcy law in geophysics. Both methods do not require any discretization and are exact methods.

In this article, we present two Monte Carlo methods to solve some problems related to the Darcy law in geophysics. Both methods do not require any discretization and are exact methods.

Classical Geostatistics methods have been designed to use mainly statistical knowledge about natural variables and they lack the ability to incorporate important forms of knowledge like physical laws and scientific theories into the mapping process. On the other hand, the powerful and versatile Bayesian maximum entropy (BME) method of Modern Geostatistics can accomplish such a task, rigorously ...

Topological groundwater hydrodynamics is an emerging subdiscipline in the mechanics of ¯uids in porous media whose objective is to investigate the invariant geometric properties of subsurface ¯ow and transport processes. In this paper, the topological characteristics of groundwater ¯ows governed by the Darcy law are studied. It is demonstrated that: (i) the topological constraint of zero helici...

This paper investigates the influence of double dispersion and viscosity on natural convection heat and mass transfer from vertical cone in a non-Darcy porous medium saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the n...

We study the existence of weak solutions to a Cahn–Hilliard–Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in Darcy’s law. The system of equations arises from a mixture model for tumour growth accounting for transport mechanisms such as chemotaxis and active transport. We prove, via a Galerkin approximation, the existence of g...

Motivated by casting of fresh concrete in reinforced concrete structures, we introduce a numerical model of a steady-state non-Newtonian fluid flow through a porous domain. Our approach combines homogenization techniques to represent the reinforced domain by the Darcy law with an interfacial coupling of the Stokes and Darcy flows through the Beavers-Joseph-Saffman conditions. The ensuing two-sc...

Here Darcy-Forchheimer flow of viscoelastic fluids has been analyzed in the presence of Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions. Results for two viscoelastic fluids are obtained and compared. A linear stretching surface has been used to generate the flow. Flow in porous media is characterized by considering the Darcy-Forchheimer model. Modified version of Fourier's l...

in this paper, fluid flow between two parallel flat plates that are partially filled with two-dimension porous media is investigated numerically using single relaxation time (srt) lattice boltzmann method (lbm) at pore scale. the considered obstacles are random, circular, rigid and granular with uniform diameters. single component and single-phase viscous newtonian fluid are considered as worki...