Stokes' first problem for a Newtonian fluid in a non-Darcian porous half-space using a Laguerre-Galerkin method

Akyildiz F. T.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.30, no.17, pp.2263-2277, 2007 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 17
  • Publication Date: 2007
  • Doi Number: 10.1002/mma.893
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2263-2277
  • Keywords: laguerre-Galerkin method, Stokes' first problem, discontinuous boundary condition, quasi-linear parabolic equation, regularized boundary layer function, DIFFERENTIAL-EQUATIONS, FLOW
  • Ondokuz Mayıs University Affiliated: No

Abstract

A Laguerre-Galerkin method is proposed and analysed for the Stokes' first problem of a Newtonian fiuid in a non-Darcian porous half-space on a semi-infinite interval. It is well known that Stokes' first problem has a jump discontinuity on boundary which is the main obstacle in numerical methods. By reformulating this equation with suitable functional transforms, it is shown that the Laguerre-Galerkin approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre-Galerkin approximations of the transformed equations is developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Copyright (c) 2007 John Wiley & Sons, Ltd.