Browse > Article
http://dx.doi.org/10.3795/KSME-B.2006.30.3.262

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

Choi Hyoung-G. (서울산업대학교 기계공학과)
Yoo Jung-Y. (서울대학교 기계항공공학부)
Park Jae-I. (현대자동차 연구개발 총괄본부 선행연구팀)
Cho Myung-H. (서울대학교 대학원 기계항공공학부)
Publication Information
Transactions of the Korean Society of Mechanical Engineers B / v.30, no.3, 2006 , pp. 262-269 More about this Journal
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
Semi-Segregation FEM; Strouhal Number; Spatial Accuracy; Pressure Boundary Condition;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 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
2 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   DOI   ScienceOn
3 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   DOI   ScienceOn
4 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   DOI   ScienceOn
5 Babuska, I., 1971, 'Errors Bounds for Finite Element Method,' Numer. Math., Vol. 16, pp. 322-333   DOI
6 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
7 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   DOI   ScienceOn
8 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
9 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   DOI   ScienceOn
10 Carey, G. F. and Oden, J. T., 1986, 'Finite Elements, Fluid Mechanics,' Vol. 6, Prentice-Hall, Englewood Cliffs, N. J., U. S. A
11 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   DOI   ScienceOn
12 Karniadakis, G. E. and Triantafyllou, G. S., 1989, 'Frequency Selection and Asymptotic States in Laminar Wakes,' J. Fluid Mech., Vol. 199, pp. 441-469   DOI   ScienceOn
13 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
14 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   DOI   ScienceOn
15 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   DOI
16 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   DOI
17 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   DOI   ScienceOn
18 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   DOI   ScienceOn
19 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   DOI   ScienceOn
20 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   DOI
21 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   DOI   ScienceOn
22 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   DOI   ScienceOn
23 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