Stokes' First Problem for a Newtonian Fluid in a Non-Darcian Porous Half-Space Using a Laguerre-Galerkin Method

Abstract

A Laguerre-Galerkin method is proposed and analysed for the Stokes' first problem of a Newtonian fluid 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 © 2007 John Wiley & Sons, Ltd.