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Development of a Numerical Model of Shallow-Water Flow using Cut-cell System  

Kim, Hyung-Jun (한양대학교 일반대학원 토목공학과)
Lee, Seung-Oh (홍익대학교 공과대학 건설도시공학부)
Cho, Yong-Sik (한양대학교 공과대학 도시건설환경공학부)
Publication Information
Journal of the Korean Society of Hazard Mitigation / v.8, no.4, 2008 , pp. 91-100 More about this Journal
Abstract
Numerical implementation with a Cartesian cut-cell method is conducted in this study. A Cartesian cut-cell method is an easy and efficient mesh generation methodology for complex geometries. In this method, a background Cartesian grid is employed for most of computational domain and a cut-cell grid is applied for the peculiar grids where the flow characteristics are changed such as solid boundary to enhance the accuracy, applicability and efficiency. Accurate representation of complex geometries can be obtained by using the cut-cell method. The cut-cell grids are constructed with irregular meshes which have various shape and size. Therefore, the finite volume method is applied to numerical discretization on a irregular domain. The HLLC approximate Riemann solver, a Godunov-type finite volume method, is employed to discretize the advection terms in the governing equations. The weighted average flux method applied on the Cartesian cut cell grid for stabilization of the numerical results. To validate the numerical model using the Cartesian cut-cell grids, the model is applied to the rectangular tank problem of which the exact solutions exist. As a comparison of numerical results with the analytical solutions, the numerical scheme well represents flow characteristics such as free surface elevation and velocities in x-and y-directions in a rectangular tank with the Cartesian and cut-cell grids.
Keywords
shallow-water equations; cut-cell method; finite volume method; HLLC approximate Riemann solver; TVD-WAF method;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 이종욱, 조용식 (2001) TVD수치모형의 개발: 천수방정식. 한국수자원학회논문집, 한국수자원학회, 제34권, pp. 187-195
2 Gao, F., Ingram, D. M., Causon, D. M. and Mingham, C. G. (2006) The development of a Cartesian cut cell method for incompressible viscous flows. Int. Journal for Numerical method in fluids, Vol. 54, pp. 1033-1053
3 Lynch, D. R. and Gray, W. G. (1978) Analytic solutions for computer flow model testing. Journal of the Hydraulic Division, ASCE, Vol. 104, No. HY10, pp. 1409-1428
4 Qian, L., Causon, D. M., Ingram, D. M. and Mingham, C. G. (2003) Cartesian cut cell two-fuid solver for hydraulic flow problems. Journal of Hydraulic Engineering. Vol. 129, pp. 688?696
5 Zhou, J. G., Causon, D. M., Mingham, C. G. and Ingram, D. M. (2004) Numerical prediction of dam-break flows in general geometries with complex bed topography. Hydraulic Engineering, Vol. 130, No. 4, pp. 332?340
6 Fraccarollo, L. and Toro, E. F. (1995) Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems. J. Hydraul. Res. Vol. 33, pp. 843-864   DOI   ScienceOn
7 Causon, D. M., Ingram, D. M., and Mingham, C. G. (2001) A Cartesian cut cell method for shallow water flows with moving boundaries. Adv. Water Resour., Vol. 24, pp. 899-911   DOI   ScienceOn
8 Toro, E. F. (1999) Riemann solvers and numerical methods for fluid dynamics. Springer
9 Ingram, D. M., Causon, D. M. and Mingham C. G. (2003) Development in Cartesian cut cell methods. Math. and Computers in simulation, Vol. 61 pp. 561-572   DOI   ScienceOn
10 김대홍, 조용식 (2005) 불규칙 지형에 적용가능한 쌍곡선형 천수 방정식을 위한 개선표면경사법. 대한토목학회논문집, 대한토목 학회, 제25권, pp. 223-229
11 Bellos, C., Soulis, J. V. and Sakkas, J. G. (1992) Experimental Investigation of Two-Dimensional Dam-Break Flows. J. of Hydraulic Research, Vol. 30, No. 1, pp. 47-63   DOI
12 Billet, S. J. and Toro, E. F. (1997) On the Accuracy and Stability of Explicit Schemes for Multidimensional Linear Homogeneous Advection Equations. Journal of Computational Physics, Vol. 131, pp. 247-250(4)   DOI   ScienceOn
13 Morris, M. (2000 CADAM: Concerted action on dambreak modeling- Final report. Rep. No. SR 571, HR Wallingford
14 전정숙, 이봉희, 조용식 (2003) TVD기법을 이용한 불연속 흐름 의 수치해석. 한국수자원학회논문집, 한국수자원학회, 제36권, pp. 597-608
15 Causon, D. M., Ingram, D. M., Mingham, C. G., Yang, G., and Pearson, R. V. (2000) Calculation of shallow water flows using a Cartesiancut cell approach. Adv. Water Resour., Vol. 23, pp. 545-562   DOI   ScienceOn
16 윤태훈, 강석구, 이지송 (2002) 본류 수위 급상승에 의한 지류 역류 해석. 대한토목학회논문집, 대한토목학회, 제22권, pp. 33-41
17 Yang, G., Causon, D. M. and Ingram, D. M. (2000) Calculation of compressible flows about complex moving geometries using a three-dimensional Cartesian cut cell method. Int. Journal for Numerical Methods in Fluids, Vol. 33, pp. 1121-1151   DOI   ScienceOn
18 Qian, L., Causon, D. M., Ingram, D. M., Mingham, C. G., and Zhou, J. G. (2001) A Cartesian cut cell method for incompressible viscous flows. Proc., European Community on Computational Methods in Applied Sciences (ECCOMAS), CFD 2001, Institute of Mathematics and its Applications, Southend-on Sea, U.K
19 김우구, 정관수, 김재한 (2003) WAF기법을 이용한 천수방정식 해석. 한국수자원학회논문집, 한국수자원학회, 제36권, pp. 777-785