A separation between the boundary shape and the boundary functions in the parametric integral equation system for the 3D Stokes equation
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The paper introduces the analytical modification of the classic boundary integral equation (BIE) for Stokes equation in 3D. The performed modification allows us to obtain separation of the approximation boundary shape from the approximation of the boundary functions. As a result, the equations, called the parametric integral equation system (PIES) with formal separation between the boundary geometry and the boundary functions, are obtained. It enables us to independently choose the most convenient methods of boundary geometry modeling depending on its complexity without any intrusion into the approximation of boundary functions and vice versa. Furthermore, we investigated the possibility of the modeling of the domains bounded by rectangular and triangular parametric Bézier patches. The boundary functions are approximated by generalized Chebyshev series. In addition, numerical techniques for solving the obtained PIES have been developed. The effectiveness of the presented strategy for boundary representation by surface patches in connection with PIES has been studied in numerical examples.
KeywordsParametric integral equation system (PIES) Boundary integral equation (BIE) Stokes equation Bézier surface patches
- 15.Becker, A.A.: The Boundary Element Method in Engineering: a Complete Course. McGraw-Hill Book Companies, Cambridge (1992)Google Scholar
- 17.Power, H., Wrobel, L.C.: Boundary integral methods in fluid mechanics. Computational Mechanics Publications (1995)Google Scholar
- 19.Zieniuk, E.: Computational method PIES for solving boundary value problems. PWN Warsaw. (in Polish) (2013)Google Scholar
- 23.Zieniuk, E., Szerszeń, K.: The PIES for solving 3D potential problems with domains bounded by rectangular bézier patches. Eng. Comput. 31(4), 791–809 (2014)Google Scholar
- 24.Zieniuk, E., Szerszeń, K.: Triangular bézier surface patches in modeling shape of boundary geometry for potential problems in 3D. Eng. Comput. 29(3), 517–527 (2013)Google Scholar
- 26.Zieniuk, E., Szerszen, K., Kapturczak, M.: A Numerical Approach to the Determination of 3D Stokes Flow in Polygonal Domains Using PIES. Lecture Notes in Computer Sciences 7203, part I, pp 112–121. Springer, Berlin (2012)Google Scholar
- 27.Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. Morgan Kaufmann Publishers, Burlington (2001)Google Scholar
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