Hermite 유동함수법에 의한 자연대류 유동 계산
Computations of Natural Convection Flow Using Hermite Stream Function Method
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초록
This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).
Abstract
This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).
참고문헌 (14)
- 김진환, "유동계산을 위한 다단계 부분 구조법에 대한 연구", 한국전산유체공학회지, 10(2), pp.38~47 (2005), 한국전산유체공학회
- 김진환, "Hermite 유동함수를 이용한 비압축성 유동계산", 한국전산유체공학회지, 12(1), pp.35~42 (2007), 한국전산유체공학회
- Botella, O., "Benchmark Spectral Results on the Lid-Driven Cavity Flow", Computers & Fluids, 27, pp.421~433 (1998)
- "Cambridge, MA, U.S.A"[URL]
- Christon, M.A., "Computational Predictability of Time-dependent Natural Convection Flows in Enclosures (Including a Benchmark Solution)", Int. J. for Numer. Methods in Fluids, 40, pp.953~980 (2002)
- De Vahl Davis, G., "Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution", Int. J. for Numer. Nethods in Fluids, 3, pp.249~264 (1983)
- Ghia, U., "High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method", J. of Comp. Physics, 48, pp.387~411 (1982)
- Griffiths, D.F., "An Approximately Divergence-Free 9-Node Velocity Element (with Variationa) for Incompressible Flows", Int. J. for Numer. Meth. in Fluids, 1, pp.323~346 (1981)
- "I. Some Lagrange Interpolation Functions for Solenoidal and Irrotational Vector Fields"[URL]
- "II. Some Hermite Interpolation Functions for Solenoidal and Irrotational Vector Fields"[URL]
- Ilinca, F., "On Stabilized Finite Element Formulations for Incompressible Advective-Diffusive Transport and Fluid Flow Problems", Comput. Methods Appl. Mech. Engrg., 188, pp.235~255 (2000)
- Lapidus, L., "Numerical Solution of Partial Differential Equations in Sciences and Engineering" (1982), John Wiley & Sons, Inc.
- Pozikidis, C., "Introduction to Theoretical and Computational Fluid Dynamics" (1977), Oxford University Press
- Shu, C., "Numerical Simulation of Natural Convection in a Square Cavity by SIMPLEGeneralized Differential Quadrature Method", Computers & Fluids, 31, pp.209~226 (2002)