We study a system composed of a non-linear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rat...

Stress waves contain useful information about the properties of porous materials; they can be recovered through different non-destructive testing methods such as crosswell, vertical seismic profile, borehole logging as well as sonic tests. In all these methods, it is crucial to assess the effects of frequency on wave attributes including velocity and intrinsic attenuation. The dependency of per...

Seepage in a medium packed with particles of variable granular size can be seen in many fields of engineering applications. Due to the relative complex spatial aspect of pore geometry, there are notable differences in the critical parameters of flow transition (Reynolds number and Forchheimer number) between different structures. It is difficult to distinguish the available range of seepage equ...

For the manufacturing of composite materials with textile reinforcement, the permeability of the textile is a key characteristic. Using the law of Darcy, permeability can be derived from a numerical simulation of the fluid flow, i.e. by solving the Navier-Stokes or Brinkman equations. In this paper we present the results of simulations with two different flow solvers: a finite difference Navier...

In this talk we consider a Darcy flow problem coupled with a deposition function. Our model arises in the context of filtration, where a fluid carrying some particulate flows through some porous medium. As the particulate deposits, the porosity of the filter changes, modifying the flow conditions. In the talk we will motivate the model, discuss the existence and uniquess of our problem, provide...

Hellman, F. 2017. Numerical Methods for Darcy Flow Problems with Rough and Uncertain Data. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1495. 41 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9872-6. We address two computational challenges for numerical simulations of Darcy flow problems: rough and uncertain data. The rapidly ...

This paper is concerned with the study of the peristaltic flow of Herschel – Bulkley fluid in an inclined flexible channel lined with porous material under long wave length and low Reynolds number assumptions. This model may be applicable to describe blood flow in the sense that erythrocytes region and the plasma regions may be described as plug flow and non-plug flow regions. The effect of yie...

The use of a constraint (indefinite) preconditioner for the iterative solution of the linear system arising from the finite element discretization of coupled Stokes–Darcy flow is studied. Spectral and field-of-values bounds for the preconditioned system which are independent of the underlying mesh size are presented. Numerical experiments on several twoand three-dimensional problems illustrate ...

The value of the permeability in fluid flow through porous media is important for process investigation. In low Reynolds number, the classic Darcy’s law is suitable for simulation of fluid flow. In this paper, an experimental study for evaluation of preformed fiber permeability has been done. Also, the deviations from the classical Darcy law by experimental and numerical simulation of the N...

In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...