constant rate of strain (crs) consolidation is a rapid test method used for determination of compressibility of clayey soils. in a crs test, the appropriate strain rate is selected based on pore water pressure ratio, i.e. the ratio of pore pressure to total stress. in the present study, to investigate the effect of strain rate on variation of relative pore water pressure, four different clay sa...

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...

Numerical approximation of stochastic Stokes–Darcy equations usually requires repeated sampling the random hydraulic conductivity tensor and then simulating flow ensembles. In this setting, we propose an efficient, second order, ensemble algorithm for fast computation whole set realizations model corresponding to different samples. The only solution two linear systems that have same constant co...

We consider a family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements (both for the pressure and the flux variable). Instead of using a jump stabilization as it is usually done for DG methods (see e.g. [3], [13] and the references therein) we use the stabilization introduced in [18], [17]. We show that such stabilization works for disconti...

We develop a finite element discretization and multigrid solver for a Darcy-Stokes system of three dimensional vuggy porous media, i.e., porous media with cavities. The finite element method uses low order mixed finite elements in the Darcy and Stokes domains, and special transition elements near the Darcy-Stokes interface to allow for tangential discontinuities implied by the Beavers-Joseph bo...

Abstract. In this paper, the Soret and Dufour effects on the steady, laminar mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a non-Darcy porous medium saturated with micropolar fluid are studied. The governing partial differential equations are transformed into ordinary differential equations. The local similarity solutions of the transformed dimensionle...

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...

In the present work, forced convection heat transfer of slip flow in porous micro-tubes with local thermal non-equilibrium between the gas and the solid matrix is investigated numerically. For this purpose, the flow is considered hydrodynamically developed but thermally developing. The Darcy-Brinkman-Forchheimer model in conjunction with separate energy equations for the gas and the solid matri...

An implementation of a coupled Navier-Stokes/Darcy model based on different Dune discretization modules is presented. The Darcy model is taken from DuMux, the Navier-Stokes model is implemented on top of Dune-PDELab, and the coupling is done with help of Dune-MultiDomain together with some project-specific auxiliary code. The Navier-Stokes model features one fluid phase, the Darcy model two flu...