Generalized finite difference method for solving the double-diffusive natural convection in fluid-saturated porous media

2018 ◽  
Vol 95 ◽  
pp. 175-186 ◽  
Author(s):  
Po-Wei Li ◽  
Wen Chen ◽  
Zhuo-Jia Fu ◽  
Chia-Ming Fan
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Saturated Porous Media ◽  
Fluid Saturated Porous Media ◽  
Double Diffusive

A Fractional Generalised Finite Difference Method to Linear Porous Media Dynamics

2016 ◽  
Vol 846 ◽  
pp. 403-408 ◽  
Author(s):  
Y.P. Zhang ◽  
D.M. Pedroso ◽  
L. Li
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Theoretical Background ◽  
Saturated Porous Media ◽  
Mesh Free ◽  
Mesh Free Method ◽  
Dynamics Simulations ◽  
Interpolation Functions

The generalised finite difference method (GFDM) is a mesh-free method for solving partial differential equations (PDEs) in non-structured grids. Due to its strong theoretical background and simplicity, hence efficiency, it has been introduced to handle interesting and sophisticate engineering problems. However, the GFDM has not been applied to problems associated to dynamics of porous media yet. In these problems, the strong coupling between solid displacements and liquid pressures may cause large numerical oscillations if equal order interpolation functions are used for both variables. Nevertheless, some fractional steps techniques can be introduced in order to minimise these problems. In this contribution, a fractional steps scheme is developed and applied to the GFDM in order to model fully saturated porous media dynamics. Simulations of 1D and 2D wave propagation are performed in order to reveal the advantages, drawbacks and capabilities of the proposed method.

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