Numerical Study of Unsteady Flow of Gas Through a Porous Medium By Means of Chebyshev Pseudo-Spectral Method

Subject Areas : International Journal of Industrial Mathematics

S. M. Hosseini Herat ¹ , E. Babolian ² , S. Abbasbandy ³

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Received: 2015-09-12 Accepted : 2017-10-21 Published : 2018-08-01

Keywords: Chebyshev pseudo-spectral method, Positive scaling factor, Newton iteration method, Chebyshev interpolation,

Abstract :

In this work, we first reformulate the unsteady flow of gas through a porous medium problem in [0,+∞) to a problem in [-1,1] by variable transformation μ = (x-s)/(x+s), and using spectral collocation method based on Chebyshev polynomials to approximate the resulting problem. The comparison of the results obtained by this method with results obtained by other methods shows that this method provides more accurate and numerically stable solutions.