Method of regularized sources for two-dimensional Stokes flow problems based on rational or exponential blobs

• Autorzy: Wen S. , Wang K. , Zahoor R. , Li M. , Šarler B.
• Języki publikacji: EN

Abstrakty

EN

The solution of Stokes flow problems with Dirichlet and Neumann boundary conditions is performed by a non-singular method of fundamental solutions (MFS) which does not require artificial boundary, i.e., source points of fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity is obtained from the analytical solution due to the action of the Dirac delta- type force. Instead of Dirac delta force, a non-singular function called blob, with a free parameter epsilon is employed, which is limited to Dirac delta function when epsilon is limited to zero. The analytical expressions for related Stokes flow pressure and velocity around such regularized sources have been derived for rational and exponential blobs in an ordered way. The solution of the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary and with their intensities chosen in such a way that the solution complies with the boundary conditions. A numerical example for two-dimensional (2D) driven cavity and a flow between parallel plates are chosen to assess the properties of the method. The results of the posed method of regularized sources (MRS have been compared with the results obtained by the fine-grid second-order classical finite difference method (FDM) and analytical solution. The results converge with finer discretisation; however, they depend on the value of epsilon. The method gives reasonably accurate results for the range of epsilon between 0.1 and 0.5 of the typical nodal distance on the boundary. Exponential blobs give slightly better results than the rational blobs; however, they require slightly more computing time. A robust and efficient strategy to find the optimal value of epsilon is needed in the perspective.

Słowa kluczowe

EN

Stokes flow; regularized sources; rational blobs; exponential blobs; meshless method; driven cavity problem; convergence study

PL

przepływ Stokesa; źródła uregulowane; racjonalne plamy; metoda bezsiatkowa; badanie zbieżności

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2015
• Tom: Vol. 22, no. 3
• Strony: 289--300
• Opis fizyczny: Bibliogr. 15 poz., wykr.

Twórcy

autor

Wen S.

• College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China

autor

Wang K.

• College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China

autor

Zahoor R.

• Laboratory for Multiphase Processes University of Nova Gorica Vipavska 13, SI-5000, Nova Gorica, Slovenia

autor

Li M.

• College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China

autor

Šarler B.

• College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China
• Laboratory for Multiphase Processes University of Nova Gorica Vipavska 13, SI-5000, Nova Gorica, Slovenia
• Laboratory for Simulation of Materials and Processes Institute of Metals and Technology Lepi pot 11, SI-1000, Ljubljana, Slovenia

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