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Method of regularized sources for axisymmetric Stokes flow problems

Kai Wang (College of Mathematics, Taiyuan University of Technology, Taiyuan, China.)
Shiting Wen (College of Mathematics, Taiyuan University of Technology, Taiyuan, China.)
Rizwan Zahoor (Laboratory for Multiphase Processes, University of Nova Gorica, Nova Gorica, Slovenia.)
Ming Li (College of Mathematics, Taiyuan University of Technology, Taiyuan, China.)
Božidar Šarler (College of Mathematics, Taiyuan University of Technology, Taiyuan, China AND Laboratory for Multiphase Processes, University of Nova Gorica, Nova Gorica, Slovenia AND Laboratory for Simulation of Materials and Processes, Institute of Metals and Technology, Ljubljana, Slovenia.)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 3 May 2016

205

Abstract

Purpose

The purpose of this paper is to find solution of Stokes flow problems with Dirichlet and Neumann boundary conditions in axisymmetry using an efficient non-singular method of fundamental solutions that does not require an artificial boundary, i.e. source points of the fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity represents analytical solution of the flow due to a singular Dirac delta source in infinite space.

Design/methodology/approach

Instead of the singular source, a non-singular source with a regularization parameter is employed. Regularized axisymmetric sources were derived from the regularized three-dimensional sources by integrating over the symmetry coordinate. The analytical expressions for related Stokes flow pressure and velocity around such regularized axisymmetric sources have been derived. The solution to the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary. The intensities of the sources are chosen in such a way that the solution complies with the boundary conditions.

Findings

An axisymmetric driven cavity numerical example and the flow in a hollow tube and flow between two concentric tubes are chosen to assess the performance of the method. The results of the newly developed method of regularized sources in axisymmetry are compared with the results obtained by the fine-grid second-order classical finite difference method and analytical solution. The results converge with a finer discretization, however, as expected, they depend on the value of the regularization parameter. The method gives accurate results if the value of this parameter scales with the typical nodal distance on the boundary.

Originality/value

Analytical expressions for the axisymmetric blobs are derived. The method of regularized sources is for the first time applied to axisymmetric Stokes flow problems.

Keywords

Acknowledgements

This research is funded by the Slovenian Research Agency under Program Group P2-0379, Bilateral Project China-Slovenia (2014-2015), and the project: innovative methods for imaging with the X-ray Free Electron Laser (XFEL) and synchrotron sources, sponsored by Desy, Germany. The project is also supported by the National Natural Science Foundation of China (Grant No. 11472184) and the National Youth Science Foundation of China (Grant No. 11401423).

Citation

Wang, K., Wen, S., Zahoor, R., Li, M. and Šarler, B. (2016), "Method of regularized sources for axisymmetric Stokes flow problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 3/4, pp. 1226-1239. https://doi.org/10.1108/HFF-09-2015-0397

Publisher

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Emerald Group Publishing Limited

Copyright © 2016, Emerald Group Publishing Limited

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