scholarly journals Effective models of the Navier–Stokes flow in porous media with a thin fissure

2012 ◽  
Vol 387 (2) ◽  
pp. 542-555 ◽  
Author(s):  
Hongxing Zhao ◽  
Zheng-an Yao
Keyword(s):  
Porous Media ◽  
Stokes Flow ◽  
Flow In Porous Media ◽  
Navier Stokes ◽  
Effective Models

Fractional vector calculus and fluid mechanics

2017 ◽  
Vol 26 (1-2) ◽  
pp. 43-54 ◽  
Author(s):  
Konstantinos A. Lazopoulos ◽  
Anastasios K. Lazopoulos
Keyword(s):  
Differential Geometry ◽  
Porous Media ◽  
Fluid Mechanics ◽  
Research Field ◽  
Flow In Porous Media ◽  
Navier Stokes ◽  
Basic Fluid ◽  
Vector Calculus ◽  
Fractional Differential ◽  
Fractional Continuum

AbstractBasic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85–104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy’s flow in porous media is studied.

Numerical Investigation of the “Poor Man’s Navier–Stokes Equations” with Darcy and Forchheimer Terms

2016 ◽  
Vol 26 (05) ◽  
pp. 1650086
Author(s):  
Tingting Tang ◽  
Zhiyong Li ◽  
J. M. McDonough ◽  
P. D. Hislop
Keyword(s):  
Porous Media ◽  
Numerical Investigation ◽  
Stokes Equations ◽  
Discrete Dynamical System ◽  
Flow In Porous Media ◽  
Phase Portraits ◽  
Navier Stokes ◽  
Flow Through Porous Media ◽  
Navier Stokes Equations ◽  
Flow Through

In this paper, a discrete dynamical system (DDS) is derived from the generalized Navier–Stokes equations for incompressible flow in porous media via a Galerkin procedure. The main difference from the previously studied poor man’s Navier–Stokes equations is the addition of forcing terms accounting for linear and nonlinear drag forces of the medium — Darcy and Forchheimer terms. A detailed numerical investigation focusing on the bifurcation parameters due to these additional terms is provided in the form of regime maps, time series, power spectra, phase portraits and basins of attraction, which indicate system behaviors in agreement with expected physical fluid flow through porous media. As concluded from the previous studies, this DDS can be employed in subgrid-scale models of synthetic-velocity form for large-eddy simulation of turbulent flow through porous media.

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