이차원 비압축성 유동 계산을 위한 Hermite 겹 3차 유동 함수법

다국어 초록 (Multilingual Abstract)

This paper is an extension of previous study [1] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite (serendipity) cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires four degrees-of-freedom at each element corners. Those degrees-of-freedom are the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational basis functions from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[2].

참고문헌 (Reference)

1 김진환, "유동계산을 위한 다단계 부분 구조법에 대한 연구" 한국전산유체공학회 10 (10): 38-47, 2005

2 Ilinca, F., "On stabilized finite element formulations for incompressible advective-diffusive transport and fluid flow problems" 188 : 235-255, 2000

3 Lapidus, L., "Numerical solution of Partial Differential Equations in Sciences and Engineering" John Wiley & Sons, Inc. 1982

4 Pozrikidis, C., "Introduction to Theoretical and Computational Fluid Dynamics" Oxford University Press 1977

5 Holdeman, J.T., "II. Some Hermite Interpolation functions for solenoidal and irrotational vector fields"

6 Ghia, U., "High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method" 48 : 387-411, 1982

7 김진환, "Hermite 유동함수를 이용한 비압축성 유동계산" 한국전산유체공학회 12 (12): 35-42, 2007

8 Botella, O., "Benchmark spectral results on the lid-driven cavity flow" 27 : 421-433, 1998

9 Hughes, T.J.R., "A Multi-dimensional upwind scheme with no crosswind diffusion" 34 : 19-35, 1979