Flow of a Fluid Through a Porous Solid Due to High Pressure Gradients

Srinivasan, Shriram; Bonito, Andrea; Rajagopal, Κ. R.

doi:10.1615/jpormedia.v16.i3.20

Cited by 22 publications

(11 citation statements)

References 28 publications

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“…(2), the pressure-dependent viscosity implies that the porous medium parameter β (drag coefficient) also varies with the pressure (see e.g. Srinivasan et al (2013)). More precisely, the exponential dependence (3) leads to a drag coefficient of the form…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefﬁcient

Pažanin

Pereira

Suárez‐Grau

2016

JAFM

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In this paper we investigate the fluid flow through a thin (or long) channel filled with a fluid saturated porous medium. We are motivated by some important applications of the porous medium flow in which the viscosity of fluids can change significantly with pressure. In view of that, we consider the generalized Brinkman's equation which takes into account the exponential dependence of the viscosity and the drag coefficient on the pressure. We propose an approach using the concept of the transformed pressure combined with the asymptotic analysis with respect to the thickness of the channel. As a result, we derive the asymptotic solution in the explicit form and compare it with the solution of the standard Brinkman's model with constant viscosity. To our knowledge, such analysis cannot be found in the existing literature and, thus, we believe that the provided result could improve the known engineering practice.

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Section: Introductionmentioning

confidence: 99%

Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefﬁcient

Pažanin

Pereira

Suárez‐Grau

2016

JAFM

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“…We refer to [50] for a generalization of the classical Brinkman equation considering the dependence on pressure of the viscosity and the drag coefficient. More precisely, in this work we are interested in the case in which the dissipation due to the drag at the pores is much larger than the dissipation due to the shear in the bulk fluid.…”

Section: Introductionmentioning

confidence: 99%

A mixed finite element method for Darcy’s equations with pressure dependent porosity

2015

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In this work we develop the a priori and a posteriori error analyses of a mixed finite element method for Darcy's equations with porosity depending exponentially on the pressure. A simple change of variable for this unknown allows to transform the original nonlinear problem into a linear one whose dual-mixed variational formulation falls into the frameworks of the generalized linear saddle point problems and the fixed point equations satisfied by an affine mapping. According to the latter, we are able to show the well-posedness of both the continuous and discrete schemes, as well as the associated Cea estimate, by simply applying a suitable combination of the classical Babuška-Brezzi theory and the Banach fixed point Theorem. In particular, given any integer k ≥ 0, the stability of the Galerkin scheme is guaranteed by employing Raviart-Thomas elements of order k for the velocity, piecewise polynomials of degree k for the pressure, and continuous piecewise polynomials of degree k+1 for an additional Lagrange multiplier given by the trace of the pressure on the Neumann boundary. Note that the two ways of writing the continuous formulation suggest accordingly two different methods for solving the discrete schemes. Next, we derive a reliable and efficient residualbased a posteriori error estimator for this problem. The global inf-sup condition satisfied by the continuous formulation, Helmholtz decompositions, and the local approximation properties of the Raviart-Thomas and Clément interpolation operators are the main tools for proving the reliability. In turn, inverse and discrete inequalities, and the localization technique based on triangle-bubble and edge-bubble functions are utilized to show the efficiency. Finally, several numerical results illustrating the good performance of both methods, confirming the aforementioned properties of the estimator, and showing the behaviour of the associated adaptive algorithm, are reported.

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“…The use of (3) allows indeed to extend models that have been investigated using the classical Darcy's law to the case of pressure dependent viscosity. Interesting applications have been described in Srinivasan, Bonito, and Rajagopal (2013) and in Nakshatrala and Rajagopal (2011). Special flows of fluid with pressure depend viscosity (even not strictly related to filtration) have been recently studied in detail (Fusi, Farina, & Rosso, 2014;Rajagopal, Saccomandi, & Vergori, 2012).…”

Section: Introductionmentioning

confidence: 99%

Mathematical models for fluids with pressure-dependent viscosity flowing in porous media

Fusi¹,

Farína²,

Rosso³

2015

International Journal of Engineering Science

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Flow of a Fluid Through a Porous Solid Due to High Pressure Gradients

Cited by 22 publications

References 28 publications

Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefﬁcient

Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefﬁcient

A mixed finite element method for Darcy’s equations with pressure dependent porosity

Mathematical models for fluids with pressure-dependent viscosity flowing in porous media

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