Czasopismo
2015
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Vol. 22, no. 3
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289--300
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
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.
Rocznik
Tom
Strony
289--300
Opis fizyczny
Bibliogr. 15 poz., wykr.
Twórcy
autor
- College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China
autor
- College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China
autor
- Laboratory for Multiphase Processes University of Nova Gorica Vipavska 13, SI-5000, Nova Gorica, Slovenia
autor
- College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China
autor
- College of Mathematics Taiyuan University of Technology Yingze West Street 79, 030024 Taiyuan, Shanxi Province, China, bozidar.sarler@ung.si
- 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
Bibliografia
- [1] D.J. Acheson. Elementary Fluid Dynamics. Oxford Applied Mathematics and Computing Science Series, Oxford, England, 1990.
- [2] K.R. Beyerlein, L. Adriano, M. Heymann, R. Kirian, J. Knoška, F. Wilde, H.N. Chapman, S. Bajt. Ceramic micro-injection molded nozzles for serial femtosecond crystallography sample delivery. Review of Scientific Instruments, 86: 125104, 2015, http://dx.doi.org/10.1063/1.4936843.
- [3] W. Chen, Z.J. Fu, C.S. Chen. Recent Advances in Radial Basis Function Collocation Methods. Springer Briefs in Applied Sciences and Technology, Springer, Heidelberg, 2014.
- [4] D.L. Young, K.H. Chen, C.W. Lee. Novel meshless method for solving the potential problems with arbitrary domain. Journal of Computational Physics, 209: 290–322, 2006.
- [5] D.L. Young, S.J. Jane, C.M. Fan, K. Murgesan, C.C. Tsai. The method of fundamental solutions for 2D and 3D Stokes problems. Journal of Computational Physics, 211: 1–8, 2006.
- [6] A.E. Curteanu, L. Elliot, D.B. Ingham, D. Lesnic. Laplacian decomposition and the boundary element method for solving Stokes problems. Engineering Analysis with Boundary Elements, 31: 501–513, 2007.
- [7] B. Šarler. Solution of potential flow problems by the modified method of fundamental solutions: formulations with the single layer and the double layer fundamental solutions. Engineering Analysis with Boundary Elements, 33: 1374–1382, 2009.
- [8] M. Perne, B. Šarler, F. Gabrovšek. Calculating transport of water from ˇ a conduit to the porous matrix by boundary distributed source method. Engineering Analysis with Boundary Elements, 36: 1649–1659, 2012.
- [9] E. Sincich, B. Šarler. Non-singular method of fundamental solutions base ˇ d on Laplace decomposition for 2D Stokes flow problems. Computer Modeling in Engineering & Sciences, 99: 393–415, 2014.
- [10] R. Cortez. The method of regularized Stokeslets. SIAM Journal of Scientific Computing, 23: 1204–1225, 2005.
- [11] R. Cortez, L. Fauci, A. Medovikov. The method of regularized Stokeslets in three dimensions: analysis, validation, and application to helical swimming. Physics of Fluids, 17: 031504–1, 031504–14, 2005.
- [12] K. Wang, S.T. Wen, R. Zahoor, M. Li, B. Šarler. Method of regularized sources for axisymmetric Stokes flow problems. International Journal of Numerical Methods for Heat & Fluid Flow, 26(3/4): 1226–1239, 2016.
- [13] A.R. Lamichhane, C.S. Chen. The closed-form particular solutions for Laplace and biharmonic operators using Gaussian radial basis function. Applied Mathematics Letters, 46: 50–56, 2015.
- [14] U. Ghia, K.T. Ghia, C.T. Shin. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48, 387–411, 1982.
- [15] C.S. Chen, A. Karageorghis, Y. Li. On choosing the location of the sources in MFS. Numerical Algorithms, DOI: 10.1007/s11075-015-0036-0, 2016.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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