Modelling the flow of a second order fluid through and over a porous medium using the volume averages. I. The generalized Brinkman’s equation

2016 ◽  
Vol 28 (2) ◽  
pp. 023102 ◽  
Author(s):  
Mario Minale
Keyword(s):  
Porous Medium ◽  
Second Order ◽  
Brinkman’S Equation

Study of Second Order(Rivlin-Ericksen) MHD Fluid Flow Due to an Impulsively Started Flat Plate Through Porous Medium

2017 ◽  
Vol 6 (1) ◽  
pp. 29-32
Author(s):  
Devendra Kumar ◽  
◽  
Rajesh Kumar Bholey Singh ◽  
R. K. Shrivastava ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flat Plate ◽  
Second Order

scholarly journals Numerical Solotion of a Problem of Fluid Filtration in a Viscoelastic Porous Medium

2020 ◽  
pp. 72-76
Author(s):  
R.A. Virts ◽  
A.A. Papin ◽  
W.A. Weigant
Keyword(s):  
Porous Medium ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Order Equation ◽  
Second Order ◽  
Initial System ◽  
Effective Pressure ◽  
Initial Boundary Value

The paper considers a model for filtering a viscous incompressible fluid in a deformable porous medium. The filtration process can be described by a system consisting of mass conservation equations for liquid and solid phases, Darcy's law, rheological relation for a porous medium, and the law of conservation of balance of forces. This paper assumes that the poroelastic medium has both viscous and elastic properties. In the one-dimensional case, the transition to Lagrange variables allows us to reduce the initial system of governing equations to a system of two equations for effective pressure and porosity, respectively. The aim of the work is a numerical study of the emerging initial-boundary value problem. Paragraph 1 gives the statement of the problem and a brief review of the literature on works close to this topic. In paragraph 2, the initial system of equations is transformed, as a result of which a second-order equation for effective pressure and the first-order equation for porosity arise. Paragraph 3 proposes an algorithm to solve the initial-boundary value problem numerically. A difference scheme for the heat equation with the righthand side and a Runge–Kutta second-order approximation scheme are used for numerical implementation.

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