Abstract
This paper discusses a generalization of intensively developed parametric integral equation system (PIES) to solve 3D steady Stokes flow. Given the preliminary nature of this research, the effectiveness of the generalized PIES has been verified for the solutions of the Stokes problems defined on polygonal domains. The boundary of such domains has been modeled directly in PIES by joining rectangular Coons parametric patches of the first degree. With them it is possible to model relatively large linear segments of the boundary by small number of corner points of the considered polygonal domain. Two numerical examples were used to validate the solutions of PIES with analytical and numerical results available in the literature.
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References
Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. Morgan Kaufmann Publishers, San Francisco (2002)
Olshanskii, M.A.: Analysis of semi-staggered Finite-difference method with application to Bingham flows. Computer Methods in Applied Mechanics and Engineering 198, 975–985 (2009)
Murugesan, K., Lo, D.C., Young, D.L.: An effcient global matrix free finite element algorithm for 3D flow problems. Communications in Numerical Methods in Engineering 21, 107–118 (2005)
Shu, C., Wang, L., Chew, Y.T.: Numerical computation of three-dimensional incompressible Navier-Stokes equations in primitive variable form by DQ method. International Journal for Numerical Methods in Fluids 43, 345–368 (2003)
Young, D.L., Jane, S.J., Lin, C.Y., Chiu, C.L., Chen, K.C.: Solution of 2D and 3D Stokes Laws using Multiquadrics Method. Engineering Analysis with Boundary Elements 28, 1233–1243 (2004)
Youngren, G.K., Acrivos, A.: Stokes flow past a particle of arbitrary shape: a numerical method of solution. Journal of Fluid Mechanics 69(2), 377–403 (1975)
Zieniuk, E.: Bezier curves in the modification of boundary integral equations (BIE) for potential boundary-values problems. International Journal of Solids and Structures 9(40), 2301–2320 (2003)
Zieniuk, E., Szerszen, K., Boltuc, A.: Globalne obliczanie calek po obszarze w PURC dla dwuwymiarowych zagadnien brzegowych modelowanych ronwnaniem Naviera-Lamego i Poissona. Modelowanie Inzynierskie 33, 181–186 (2007) (in Polish)
Zieniuk, E., Boltuc, A.: Bezier curves in the modeling of boundary geometries for 2D boundary problems defined by Helmholtz equation. Journal of Computational Acoustics 3(14), 1–15 (2006)
Zieniuk, E., Boltuc, A.: Non-element method of solving 2D boundary problems defined on polygonal domains modeled by Navier equation. International Journal of Solids and Structures 43, 7939–7958 (2006)
Zieniuk, E., Szerszen, K.: Liniowe platy powierzchniowe Coonsa w modelowaniu wielokatnych obszarow w trojwymiarowych zagadnieniach brzegowych definiowanych rownaniem Laplace’a. Archiwum Informatyki Teoretycznej i Stosowanej, Instytut Informatyki Teoretycznej i Stosowanej Polskiej Akademii Nauk 17, 127–142 (2005) (in Polish)
Zieniuk, E., Szerszen, K.: Triangular Bezier patches in modelling smooth boundary surface in exterior Helmholtz problems solved by PIES. Archives of Acoustics 1(34), 1–11 (2009)
Zieniuk, E., Szerszen, K.: Trojkatne platy powierzchniowe w modelowaniu gladkiej powierzchni brzegu w PURC dla zagadnien ustalonego przepywu cieczy doskonalej. Modelowanie Inynierskie 37, 289–296 (2009) (in Polish)
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Zieniuk, E., Szerszen, K., Kapturczak, M. (2012). A Numerical Approach to the Determination of 3D Stokes Flow in Polygonal Domains Using PIES. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2011. Lecture Notes in Computer Science, vol 7203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31464-3_12
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DOI: https://doi.org/10.1007/978-3-642-31464-3_12
Publisher Name: Springer, Berlin, Heidelberg
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