Numerical study of double-diffusive natural convective heat transfer in a curved cavity filledwith a porous medium has been carried out in the current study. Polar system has beenselected as coordinate system. As a result, all equations have been discredited in r and θdirections. Brinkmann extended Darcy model has been utilized to express fluid flow inporous matrix in the enclosure. Smaller and...

In this article we investigate the numerical approximation of the Darcy equations in an axisymmetric domain, subject to axisymmetric data. Rewriting the problem in cylindrical coordinates reduces the 3-D problem to a problem in 2-D. This reduction to 2-D requires the numerical analysis to be studied in suitably weighted Hilbert spaces. In this setting the Raviart-Thomas (RT) and Brezzi-Douglas-...

In this report, a partitioned time stepping algorithm for transient flow in a porous medium coupled to a free flow in embedded conduits is analyzed. The coupled flow is modeled by the fully evolutionary Stokes-Darcy problem. This method requires only solve one, uncoupled Stokes and Darcy sub-physics and subdomain per time step. On the interface between the matrix and conduit, Beavers-Joseph int...

We propose a novel second order in time, decoupled and unconditionally stable numerical scheme for solving the Cahn-Hilliard-Darcy (CHD) system which models two-phase flow in porous medium or in a Hele-Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn-Hilliard equation and pressure-correction for the Darcy equation. We show that the scheme is uniquely sol...

for non-darcy flow in submerged porous media a one- dimensional mathematical model has been developed. rockfill detention dams are one of these porous media that comprised of relatively homogenous coarse rockfill which can be used to reduce flood discharge and hydrograph peak. in this research the focus was on the rockfill detention dams in submerged condition. the existence of overtopping rock...

The Forchheimer equation is widely used in studying non-Darcy flow. Non-Darcy flow coefficient β the generally thought to be positive, and there are few studies on negative values. In this work, we performed seepage tests sandstone samples with single, T-shaped, Y-shaped fractures under different confining pressures, water angles analyze nonlinear behaviors features of Forchheimer’s coefficient...

The gas transport in shale nanopores is always one of the major concerns in terms of the development of shale gas reservoirs. In this study, the gas flow regimes in shale nanopores were classified and analyzed according to Knudsen number. Then the gas flow model considering Darcy flow, slip flow, transition flow, molecular free flow and adsorption effect was proposed to evaluate the gas flow be...

A . This report analyzes the long time stability of four methods for non-iterative, sub-physics, uncoupling for the evolutionary Stokes-Darcy problem. The four methods uncouple each time step into separate Stokes and Darcy solves using ideas from splitting methods. Three methods uncouple sequentially while one is a parallel uncoupling method. We prove long time stability of four splitting based...

We developed two new EOS additions to the TOUGH+ family of codes, the RealGasH2O and RealGas. The RealGasH2O EOS option describes the non-isothermal two-phase flow of water and a real gas mixture in a gas reservoir (including a tight/shale gas one). The gas mixture is treated as either a single-pseudocomponent having a fixed composition, or as a multicomponent system composed of up to 9 individ...

This paper presents studies on applying the novel weak Galerkin finite element method (WGFEM) to a two-phase model for subsurface flow, which couples the Darcy equation for pressure and a transport equation for saturation in a nonlinear manner. The coupled problem is solved in the framework of operator decomposition. Specifically, the Darcy equation is solved by theWGFEM, whereas the saturation...