We consider a covolume method for a system of first order PDEs resulting from the mixed formulation of the variable-coefficient-matrix Poisson equation with the Neumann boundary condition. The system may be used to represent the Darcy law and the mass conservation law in anisotropic porous media flow. The velocity and pressure are approximated by the lowest order Raviart-Thomas space on rectang...

A new type of in-situ hydraulic permeameter was developed to determine vertical hydraulic conductivity (VHC) of saturated sediments from hydraulic experiments using Darcy's law. The system allows water to move upward through the porous media filled in the permeameter chamber driven into sediments at water-sediment interface. Darcy flux and hydraulic gradient can be measured using the system, an...

Non-Darcy behavior is important for describing fluid flow in porous media in situations where high velocity occurs. A criterion to identify the beginning of non-Darcy flow is needed. Two types of criteria, the Reynolds number and the Forchheimer number, have been used in the past for identifying the beginning of non-Darcy flow. Because each of these criteria has different versions of definition...

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 ...

There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of contaminants has, however, focused on a quasi-static Stokes-Darcy model. Herein we consider the fully evolutio...

The infinite Darcy-Prandtl number model is an effective reduced model for describing convection in a fluid-saturated porous medium. It is well known that the deterministic model does not possess a unique invariant measure. In this work we study the dynamics of the infinite Darcy-Prandtl number model, under an additive stochastic forcing of its low modes. This is the so-called stochastic infinit...

This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one c...