Unsteady flow of gas in a semi-infinite porous medium: a numerical investigation by using RBF-DQM

Abstract

The study aims to investigate how an effective numerical algorithm can be used to solve the unsteady isothermal flow of gas through a semi-infinite micro-nano porous medium. The unsteady gas equation used here is a nonlinear, second order differential equation with two points of boundary value on the semi-infinite domain. The study uses RBFs-DQ method in which the derivative value of function with respect to the point is directly approximated by a linear combination of all functional values in the entire domain. The main purpose of using this method is to determine the weight of coefficients. The study also used Gaussian (GS) function to approximate the solution of the mentioned equation. The efficiency and accuracy of this method are verified by the comparison made between our results and other numerical methods including shooting method, RBF.G and Wavelet Legendre collocation method. As a results, by comparison made to other numerical methods this showed a Meshfree (RBF-DQ) method which its validity is equal or even more valid than numerical methods.