Stokes' first problem for a Newtonian fluid in a non‐Darcian porous half‐space using a Laguerre–Galerkin method |
| |
Authors: | F Talay Akyildiz |
| |
Institution: | Department of Mathematics, Arts and Science Faculty, Ondokuz Mayis University, TurkeyDepartment of Mathematics, Arts and Science Faculty, Ondokuz Mayis University, Turkey=== |
| |
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. |
| |
Keywords: | Laguerre– Galerkin method Stokes' first problem discontinuous boundary condition quasi‐linear parabolic equation regularized boundary layer function |
|
|