This article analyses the convergence of the Vertex Approximate Gradient (VAG) scheme recently introduced in Eymard et al. 2012 for the discretization of multiphase Darcy flows on general polyhedral meshes. The convergence of the scheme to a weak solution is shown in the particular case of an incompressible immiscible two-phase Darcy flow model with capillary diffusion using a global pressure f...

A local interpolation operator, preserving the divergence, is constructed explicitly, which is the first ever one for the divergence-free elements. A divergence-free finite element method is applied to the Darcy-Stokes-Brinkman flow in a mixed region of both free and porous medium. The method is of optimal order in contrast to the traditional H and H mixed finite elements, which work for either...

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 ...

This paper formulates and analyzes a weak solution to the coupling of time-dependent Navier-Stokes flow with Darcy flow under certain boundary conditions, one of them being the Beaver-Joseph-Saffman law on the interface. Existence and a priori estimates for the weak solution are shown under additional regularity assumptions. We introduce a fully discrete scheme with the unknowns being the Navie...

This report analyzes a partitioned time stepping algorithm, meaning a non-iterative, domain decomposition method, which allows different time steps in the fluid region and the porous region for the fully evolutionary Stokes-Darcy problem. The method presented requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a time step restriction of the form 4...

We numerically investigate the pulsatile flow and heat transfer of a micropolar fluid through a Darcy-Forchhmeir porous channel in the presence of wall transpiration. We use the central difference approximations for the spatial derivatives, whereas the time integration has been performed by employing the three steps explicit Runge-Kutta method to obtain the numerical solution. It i...

Em seu centenário, como uma forma de reconhecer e rememorar engajamento político, social intelectual, a Revista Cadernos Campo propôs o dossiê especial “O centenário Darcy Ribeiro” organizado pelo editor João Victtor Gomes Varjão. Este tematiza sua obra, luta bem como, influência decisiva ao pensamento brasileiro contemporâneo. O objetivo central do foi apresentar analisar obra desse importante...

We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes--Darcy problem. Three different formulations their discretizations in terms of conforming nonconforming finite element methods volume are considered. In each case, robust preconditioners derived using a unified theoretical framework. particular, suggested utilize operators fractional Sobolev spac...