Darcy's law and the differential equation of motion

Géotechnique ◽  
2009 ◽  
Vol 59 (6) ◽  
pp. 551-552 ◽  
Author(s):  
J.J. NADER
Keyword(s):  
Differential Equation ◽  
Darcy’S Law ◽  
Equation Of Motion ◽  
Darcy's Law

scholarly journals An extension of Darcy’s law incorporating dynamic length scales

2019 ◽  
Vol 129 ◽  
pp. 70-79 ◽  
Author(s):  
Yuhang Wang ◽  
Saman A. Aryana ◽  
Myron B. Allen
Keyword(s):  
Darcy’S Law ◽  
Darcy's Law ◽  
Length Scales ◽  
Dynamic Length

scholarly journals The Use of Nonlinear Constitutive Equations to Evaluate Draw Resistance and Filter Ventilation

2001 ◽  
Vol 19 (4) ◽  
pp. 177-188
Author(s):  
B Eitzinger ◽  
G Ederer
Keyword(s):  
Pressure Drop ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Constitutive Equations ◽  
Darcy’S Law ◽  
Stationary Flow ◽  
Darcy's Law ◽  
Nonlinear Behaviour ◽  
Cigarette Paper ◽  
Drop Flow

AbstractThis study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.

The Numerical Methods of Peridynamics Theory Used in Failure Analysis of Materials

2014 ◽  
Vol 1030-1032 ◽  
pp. 223-227
Author(s):  
Lin Fan ◽  
Song Rong Qian ◽  
Teng Fei Ma
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Numerical Integration ◽  
Integration Method ◽  
Equation Of Motion ◽  
Numerical Integration Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Method Of Molecular Dynamics ◽  
Classic Theory

In order to analysis the force situation of the material which is discontinuity,we can used the new theory called peridynamics to slove it.Peridynamics theory is a new method of molecular dynamics that develops very quickly.Peridynamics theory used the volume integral equation to constructed the model,used the volume integral equation to calculated the PD force in the horizon.So It doesn’t need to assumed the material’s continuity which must assumed that use partial differential equation to formulates the equation of motion. Destruction and the expend of crack which have been included in the peridynamics’ equation of motion.Do not need other additional conditions.In this paper,we introduce the peridynamics theory modeling method and introduce the relations between peridynamics and classic theory of mechanics.We also introduce the numerical integration method of peridynamics.Finally implementation the numerical integration in prototype microelastic brittle material.Through these work to show the advantage of peridynamics to analysis the force situation of the material.

scholarly journals Simulation of Water Filtration in Porous Zone Based on Darcy's Law

2013 ◽  
Vol 36 ◽  
pp. 163-168
Author(s):  
Mohammed Amine Kendouci ◽  
Benali Kharroubi ◽  
Rachid Khelfaoui ◽  
Ali Bendida ◽  
Brahim Dennai ◽  
...  
Keyword(s):  
Darcy’S Law ◽  
Darcy's Law ◽  
Water Filtration ◽  
Porous Zone
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