Numerical simulation of incompressible flows through granular porous media

Bourchtein, Andrei; Bourchtein, Lioudmila; Lukaszczyk, João Paulo

doi:10.1016/s0168-9274(01)00072-1

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…Then, the Navier-Stokes equations (12) are discretized at the corresponding velocity nodes using forward finite differences for the time derivative, a higher-order upwinding scheme (VONOS [66]) for the inertial terms and central differencing for the viscous and pressure terms. Only the Darcy term is taken implicit in time to increase the stability of the scheme [4]. Further, the continuity equation (11) is discretized using central differences and is combined with the discretized Navier-Stokes equations to result in a discrete Poisson equation for the pressure, which is solved using the BiCGSTAB iterative method [2].…”

Section: Step 6: Determination Of the Flow Fieldmentioning

confidence: 99%

Hierarchical simulator of biofilm growth and dynamics in granular porous materials

Kapellos

Alexiou

Payatakes

2007

Advances in Water Resources

101

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Section: Step 6: Determination Of the Flow Fieldmentioning

confidence: 99%

Hierarchical simulator of biofilm growth and dynamics in granular porous materials

Kapellos

Alexiou

Payatakes

2007

Advances in Water Resources

101

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Numerical study of lid‐driven flow in orthogonal and skewed porous cavity

Krishna

Basak

Das

2007

Commun. Numer. Meth. Engng.

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SUMMARYEffects of Reynolds number, Darcy number, porosity, aspect ratio and skewness are studied in detail for liddriven cavity flows filled with fluid-saturated porous medium. A generalized non-Darcy approach has been considered to account for linear and non-linear drag forces. The governing equations are solved by using finite volume method. A quadrilateral cell in a semi-staggered arrangement has been employed and is transformed into a standard square element using local body-fitting co-ordinates by co-ordinate transformation. Details of the flow physics reveal that by the reduction of Darcy number, the primary vortex becomes weaker and tends to move towards the lid. As a measure of volume flow rate maximum stream function value is considered. It is found that, with the reduction in Darcy number and with the increase in Reynolds number and skewness the maximum stream function value reduces.

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Stokes Problem for the Generalized Navier-Stokes Equations

Bourchtein

2002

Lecture Notes in Computer Science

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Abstract. The generalized Navier-Stokes equations for incompressible viscous flows through isotropic granular porous medium are considered. First Stokes problem is solved applying Laplace transform with respect to time variable and evaluating the inverse transform integrals by the residue calculus. The derived analytical solution includes the classic one as a particular case, that is, it can be obtained from the generalized solution by putting the porosity parameter equal to 1. The use of the derived exact solutions for benchmarking purposes is described.

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Numerical simulation of incompressible flows through granular porous media

Cited by 3 publications

References 13 publications

Hierarchical simulator of biofilm growth and dynamics in granular porous materials

Hierarchical simulator of biofilm growth and dynamics in granular porous materials

Numerical study of lid‐driven flow in orthogonal and skewed porous cavity

Stokes Problem for the Generalized Navier-Stokes Equations

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