We investigate the model problem of flow of a viscous incompressible fluid past a symmetric curved surface when the flow is parallel to its axis. This problem is known to exhibit boundary layers. Also the problem does not have solutions in closed form, it is modelled by boundary‐layer equations. Using a self‐similar approach based on a Blasius series expansion (up to three terms), the boundary‐layer equations can be reduced to a Blasius‐type problem consisting of a system of eight third‐order ordinary differential equations on a semi‐infinite interval. Numerical methods need to be employed to attain the solutions of these equations and their derivatives, which are required for the computation of the velocity components, on a finite domain with accuracy independent of the viscosity v, which can take arbitrary values from the interval (0,1]. To construct a robust numerical method we reduce the original problem on a semi‐infinite axis to a problem on the finite interval [0, K], where K = K(N) = ln N. Employing numerical experiments we justify that the constructed numerical method is parameter robust.
Ansari, A. R., Hossain, B., Koren, B., & Shishkin, G. I. (2006). Robust numerical methods for boundary‐layer equations for a model problem of flow over a symmetric curved surface. Mathematical Modelling and Analysis, 11(4), 365-378. https://doi.org/10.3846/13926292.2006.9637324
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.