Numerical study on gas flow through a micro–nano porous medium based on finite difference schemes on quasi-uniform grids

Abstract

In this paper, the unsteady isothermal flow of a gas through a semi-infinite micro–nano porous medium described by a non-linear two-point boundary value problem on a semi-infinite interval has been considered. We solve this problem by a nonstandard finite difference method defined on quasi-uniform grids in order to derive a new numerical approximation. By introducing a stencil that is constructed in such a way that the boundary conditions at infinity are exactly assigned, the proposed method is effectively used to determine the numerical solution. In addition, a mesh refinement and the Richardson’s extrapolation allow to improve the accuracy of the numerical solution and to define a posteriori estimator for the global error of the proposed numerical scheme. We determine the accurate initial slope dudx(0)=−1.1917906497194208 calculated for α=0.5 with good capturing the essential behavior of u(x). This clearly demonstrates that the numerical solutions presented in this paper result highly accurate and in excellent agreement with the existing solutions available in the literature.