Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Study on the Segregation Algorithms of the Incompressible Navier-Stokes Equations Using P1P1/P2P1 Finite Element Formulation

P1P1/P2P1 유한요소 공식을 이용한 배압축성 Navier-Stokes 방정식의 분리 해법에 대한 연구

  • 최형권 (서울산업대학교 기계공학과) ;
  • 유정열 (서울대학교 기계항공공학부) ;
  • 박재인 (현대자동차 연구개발 총괄본부 선행연구팀) ;
  • 조명환 (서울대학교 대학원 기계항공공학부)
  • Published : 2006.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

Segregation algorithms of the incompressible Wavier-Stokes equations using P1P1/P2P1 finite element formulation are newly proposed. P1P1 formulation allocates velocity and pressure at the same nodes, while P2P1 formulation allocates pressure only at the vertex nodes and velocity at both the vertex and the midpoint nodes. For a comparison of both the elapsed time and the accuracy between the two methods, they have been applied to the well-known benchmark problems. The three cases chosen are the two-dimensional steady and unsteady flows around a fixed cylinder, decaying vortex, and impinging slot jet. It is shown that the proposed P2P1 semi-segregation algorithm performs better than the conventional P1P1 segregation algorithm in terms of both accuracy and computation time.

Keywords

References

  1. Tezduyar, T. E., Liou, J. and Ganjoo, D. K., 1990, 'Incompressible Flow Computations Based on the Vorticity-Stream Function and Velocity-Pressure Formulations,' Comput. & Structures, Vol. 35, pp. 445-472 https://doi.org/10.1016/0045-7949(90)90069-E
  2. Tezduyar, T. E., Mittal, S. and Shih, R., 1991, 'Time-Accurate Incompressible Flow Computations with Quadrilateral Velocity-Pressure Elements,' Comput. Methods Appl. Mech. Engrg., Vol. 87, pp. 363-384 https://doi.org/10.1016/0045-7825(91)90014-W
  3. Brooks, A. N. and Hughes, T. J. R., 1982, 'Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations,' Comput. Methods Appl. Mech. Engrg., Vol. 32, pp. 199-259
  4. Codina, R., Onate, E. and Cervera, M., 1992, 'The Intrinsic Time for the Streamline Upwind/Petrov-Galerkin Formulation Using Quadratic Elements,' Comput. Methods Appl. Mech. Engrg., Vol. 94, pp. 239-262 https://doi.org/10.1016/0045-7825(92)90149-E
  5. Choi, H. G., Choi, H. and Yoo, J. Y., 1997, 'A Fractional Four-Step Finite Element Formulation of the Unsteady Incompressible Navier-Stokes Equations Using SUPG and Linear Equal-Order Element Methods,' Comput. Methods Appl. Mech. Engrg., Vol. 143, pp. 333-348
  6. Ramaswamy, B. and Jue, T. C., 1992, 'Some Recent Trends and Developments in Finite Element Analysis for Incompressible Thermal Flows,' Internat. J. Numer. Methods Engrg., Vol. 35, pp. 671-707 https://doi.org/10.1002/nme.1620350405
  7. Tabarrok, B. and Su, J., 1994, 'Semi-Implicit Taylor-Galerkin Finite Element Methods for Incompressible Viscous Flows,' Comput. Methods Appl. Mech. Engrg., Vol. 117, pp. 391-410 https://doi.org/10.1016/0045-7825(94)90125-2
  8. Hanby, R. F., Silvester, D. J. and Chew, J. W., 1996, 'A Comparison of Coupled and Segregated Iterative Solution Techniques for Incompressible Swirling Flow,' Internat. J. Numer. Methods Fluids, Vol. 22, pp. 353-373 https://doi.org/10.1002/(SICI)1097-0363(19960315)22:5<353::AID-FLD327>3.0.CO;2-Z
  9. Nam, Y. S., Choi, H. G. and Yoo, J. Y., 2002, 'AILU Preconditioning for the Finite Element Formulation of the Incompressible Navier-Stokes Equations,' Comput. Methods Appl. Mech. Engrg., Vol. 191, pp. 4323-4339 https://doi.org/10.1016/S0045-7825(02)00369-9
  10. Choi, H. and Moin, P., 1994, 'Effects of the Computational Time Step on Numerical Solutions of Turbulent Flow,' J. Comput. Phys., Vol. 113, pp. 1-4 https://doi.org/10.1006/jcph.1994.1112
  11. Kim, B. J., Kang, S. W., Choi, H. G. and Yoo, J. Y., 2003, 'Numerical Study on the Drag of a Car Model Under Road Condition,' Trans. of the KSME (B), Vol. 27, No. 8, pp. 1182-1190 https://doi.org/10.3795/KSME-B.2003.27.8.1182
  12. Namkoong, K., Choi, H. G. and Yoo, J. Y., 2004, 'Numerical Analysis of Two-Dimensional Motion of a Freely Falling Circular Cylinder in an Infinite Fluid,' Trans. of the KSME (B), Vol. 28, No. 6, pp. 713-725 https://doi.org/10.3795/KSME-B.2004.28.6.713
  13. Williamson, C. H. K., 1989, 'Oblique and Parallel Modes of Vortex Shedding in the Wake of a Circular Cylinder at Low Reynolds Numbers,' J. Fluid Mech., Vol. 206, pp. 579-627 https://doi.org/10.1017/S0022112089002429
  14. Braza, M., Chassaing, P. and Ha Minh, H., 1986, 'Numerical Study and Physical Analysis of the Pressure and Velocity Fields in the Near Wake of a Circular Cylinder,' J. Fluid. Mech., Vol. 165, pp. 79-130 https://doi.org/10.1017/S0022112086003014
  15. Karniadakis, G. E. and Triantafyllou, G. S., 1989, 'Frequency Selection and Asymptotic States in Laminar Wakes,' J. Fluid Mech., Vol. 199, pp. 441-469 https://doi.org/10.1017/S0022112089000431
  16. Kwon, K. and Choi, H., 1994, 'A Passive Control of Vortex Shedding Using a Splitter Plate Attached to a Circular Cylinder,' Proceedings of the KSME 1994 Fall Annual Meeting, pp. 502-507
  17. Kim, D. and Choi, H., 2000, 'A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids,' J. Comput. Phys., Vol. 162, pp. 411-428 https://doi.org/10.1006/jcph.2000.6546
  18. Becker, E. B., Carey, G. F. and Oden, J. T., 1983, 'Finite Elements, an Introduction,' Vol. 1, Prentice-Hall, Englewood Cliffs, N. J., U. S. A
  19. Cziesla, T., Tandogan, E. and Mitra, N. K., 1997, 'Large-Eddy Simulation of Heat Transfer from Impinging Slot Jets,' Numerical Heat Transfer, Part A, Vol. 32, pp. 1-17 https://doi.org/10.1080/10407789708913876
  20. Carey, G. F. and Oden, J. T., 1986, 'Finite Elements, Fluid Mechanics,' Vol. 6, Prentice-Hall, Englewood Cliffs, N. J., U. S. A
  21. Babuska, I., 1971, 'Errors Bounds for Finite Element Method,' Numer. Math., Vol. 16, pp. 322-333 https://doi.org/10.1007/BF02165003
  22. Brezzi, F., 1976, 'On the Existence, Uniqueness and Approximation of Saddle Point Problems Arising from Lagrange Multipliers.' RAIRO, Ser. Rouge Anal. Numer. Vol. 8, R-2
  23. Hughes, T. J. R., Franca, L. P. and Balestre, M., 1986, 'A New Finite Element Formulation for Computational Fluid Dynamics: V. Circumventing the Babuska-Brezzi Condition: A Stable Petrov-Galerkin Formulation of Stokes Problem Accommodating Equal Order Interpolations,' Comput. Methods Appl. Mech. Engrg., Vol. 59, pp. 85-99 https://doi.org/10.1016/0045-7825(86)90025-3