On the equation describing the transient flow of a compressible liquid through deformable porous media

1978 ◽  
Vol 56 (6) ◽  
pp. 691-695
Author(s):  
B. S. BačlićF ◽  
D. P. Sekulić
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Porous Media ◽  
Transient Flow ◽  
A Priori ◽  
Nonlinear Partial Differential Equation ◽  
Compressible Liquid ◽  
Deformable Porous Media ◽  
The Mathematical Model

The effect of the linearized treatment of the equation describing the transient flow of a compressible liquid through elastic porous media is studied analytically in this paper. It is shown that if there is a need for a simplified description based on the linearization of the original nonlinear partial differential equation, then it has to be done in an optimal sense. However, even then the mathematical model may degenerate for certain boundary conditions and some values of parameters defining the dependence of fluid and media properties on pressure. This fact is illustrated by the help of a simple example of transient filtration in a semi-infinite Hookeian medium. The reliability and adequateness of the a priori linearized equation is discussed.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

Unsteady Flow of Gas Through a Semi-Infinite Porous Medium

1957 ◽  
Vol 24 (3) ◽  
pp. 329-332
Author(s):  
R. E. Kidder
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Porous Medium ◽  
Gas Flow ◽  
Transient Flow ◽  
Order Term ◽  
Nonlinear Partial Differential Equation ◽  
Flow In Porous Media ◽  
Partial Differential ◽  
One Dimensional

Abstract This paper presents an analytic solution to a problem of the transient flow of gas within a one-dimensional semi-infinite porous medium. A perturbation method, carried out to include terms of the second order, is employed to obtain a solution of the nonlinear partial differential equation describing the flow of gas. The zero-order term of the solution represents the solution of the linearized partial differential equation of gas flow in porous media given by Green and Wilts (1).

scholarly journals An Analysis on Groundwater Recharge by Mathematical Model in Inclined Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Shreekant P. Pathak ◽  
Twinkle Singh
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Porous Media ◽  
Boundary Conditions ◽  
Groundwater Flow ◽  
Groundwater Recharge ◽  
Partial Differential ◽  
One Dimensional ◽  
Graphical Interpretation

The present paper discusses the analysis of solution of groundwater flow in inclined porous media. The problem related to groundwater flow in inclined aquifers is usually common in geotechnical and hydrogeology engineering activities. The governing partial differential equation of one-dimensional groundwater recharge problem has been formed by Dupuit's assumption. Three cases have been discussed with suitable boundary conditions and different slopes of impervious incline boundary. The numerical as well as graphical interpretation has been given and its coding is done in MATLAB.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

Modelling Turbulent Flow in Deformable Highly Porous Seabed and Structures

2018 ◽  
Author(s):  
Hisham Elsafti ◽  
Hocine Oumeraci
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Stokes Equations ◽  
Pore Fluid ◽  
Navier Stokes ◽  
Model Parameters ◽  
Navier Stokes Equations ◽  
Deformable Porous Media ◽  
Physical Experiments ◽  
Fluid Coupling

In this study, the fully-coupled and fully-dynamic Biot governing equations in the open-source geotechFoam solver are extended to account for pore fluid viscous stresses. Additionally, turbulent pore fluid flow in deformable porous media is modeled by means of the conventional eddy viscosity concept without the need to resolve all turbulence scales. A new approach is presented to account for porous media resistance to flow (solid-to-fluid coupling) by means of an effective viscosity, which accounts for tortuosity, grain shape and local turbulences induced by flow through porous media. The new model is compared to an implemented extended Darcy-Forchheimer model in the Navier-Stokes equations, which accounts for laminar, transitional, turbulent and transient flow regimes. Further, to account for skeleton deformation, the porosity and other model parameters are updated with regard to strain of geomaterials. The presented model is calibrated by means of available results of physical experiments of unidirectional and oscillatory flows.

Sign in / Sign up

Export Citation Format

Share Document