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Korea Water Resources Association (한국수자원학회)
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Application Ranges of Finite Difference Models Using Simplified Momentum Equation in Channel Flow simulation

하천흐름 해석에서 단순화된 운동방정식을 사용한 유한차분모델의 신뢰성 있는 적용 범위

  • Choi, Gye-Woon (Dept.of Civil Engineering, University of Incheon) ;
  • Ahn, Kyung-Soo (Dept.of Civil Engineering, University of Incheon) ;
  • Ahn, Sang-Jin (Dept. of Civil Engineering, Engineering Collage, Chungbuk National University)
  • 최계운 (인천대학교 공과대학 토목공학과) ;
  • 안경수 (인천대학교 공과대학 토목공학과) ;
  • 안상진 (충북대학교 공과대학 토목공학과)
  • Published : 1994.12.01
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Abstract

The kinematic and diffusion models using simplified momentum equations of the full dynamic equation have been frequently used for numerical flow simulations, because they have several computational advantages compared to the full dynamic model. In this paper, the more generally acceptable application ranges of the kinematic and diffusion finite difference models were investigated based on three major parameters, which are channel bed slopes So, dimensionless depth increasing numbers Gw at upstream boundary and Froude numbers Fr. The applicable ranges were obtained by comparing the relative magnitudes of the local acceleration, convective acceleration, pressure, gravity and friction terms in the full dynamic equation. In the simulations, a Courant number of 0.5 was used and the channel bed slopes were changed from 0.00001 to 0.05. Also, Froude numbers of 0.1, 0.5 and 0.9 were employed. In this paper, it is indicated that the applicable ranges of kinematic models are increased with increasing of Froude numbers. However, the applicable ranges of diffusion models are decreased with increasing of Froude numbers. Finally, 9 figures were proposed as a guideline in the application of kinematic and diffusion finite difference models based upon the allowable deviation compared to the full dynamic model. With applying the proposed criteria, it is expected that the flow simulations in the channels, streams or rivers are more efficiently achieved.

하천 흐름해석에서 단순화된 운동방정식을 사용한 kinematic 모델과 diffusion 모델이 full dynamic 모델에 비하여 여러 장점을 지니고 있기 때문에 수치모의에 종종 사용된다. 본 논문에서는 kinematic 모델과 diffusion 모델의 적용범위에 대하여 보다 폭넓게 사용될 수 있는 적용한계를 하천의 수로경사 $S_{02}$, 무차원의 상류측 수심증가 수 Gw 및 Froude수 Fr등 3개의 주요한 인자를 기준으로 하여 연구하였다. 이 때 적용범위는 full dynamic 방정식의 시간 가속도항, 공간 가속도항, 압력항, 중력항 및 마찰항의 상대적 크기의 비교를 통하여 도출되었다. 실험모의중에 Courant수는 0.5로 한정되었으며, 하천의 하상경사는 0.00001부터 0.05까지 변하였다. 또한, 0.1, 0.5 및 0.9의 Froude 수가 사용되었다. 본 논문에서는 kinematic 모델의 적용범위는 Froude 수가 증가함에 따라 증가하는 것으로 나타났으나, diffusion 모델의 적용범위는 Froude 수가 증가함에 따라 감소하였다. 최종적으로 kinematic 모델과 diffusion 모델의 적용을 위한 지침으로 사용할 수 있는 9개의 그림이 제안되었으며 이 제안된 그림을 적절하게 활용할 때 하천이나 강에 흐름모의가 보다 효율적으로 이루어질 수 있을 것이다.

Keywords

References

  1. Pitman Advanced Publishing Program(18th Edition) Computational Hydraulics Abbott,M.B.
  2. Journal of Hydraulics no.12 Implicit Flood Routing in Natural Channels Amein,M.;Fang,C.S.
  3. Water Resources Research no.4 An Implicit Method for Numerical Flood Routing Amein,M.
  4. Journal of Hydraulics Division v.95 no.HY4 One-Dimensional Analysis of Floods and Tides in Open Channels Balloffet,A.
  5. Transactions, ASAE v.10 no.3 Kinematic Flood Routing Brakensiek,D.L.
  6. Ph. D. Dissertation, Colorado State University Mathematical Modeling of Water and Sediment Routing in Natural Channels Chen,Y.H.
  7. Ph. D. Dissertation, Dept. of Civil Engineering, Colorado State University Hydrodynamic Network Simulation Through Channel Junctions Choi,G.W.
  8. Journal of Hydraulics Division no.7 Implicit Flood Routing in Natural Channels Fread,D.L.
  9. Hydraulic Engineering Laboratory Report no.1 Wave Propagation in Rivers Harder,J.A.;Armacost,L.V.
  10. Journal of Hydraulics Division v.89 no.HY4 Flood Waves in Prismatic Channels Henderson,F.M.
  11. Open Channel Flow Henderson,F.A.
  12. Proceedings., International Hydrology Symposium Flood Forecasting in the River Kitakami Iwasaki,T.
  13. Chapter 4 of Unsteady Flow in Open Channels Numerical Methods of Solution of the Unsteady Flow Equations Liggett,J.A.;Cunge,J.A.;Mahmood,K.(ed.);Yevjevich,V.(ed.)
  14. Journal of Hydraulics no.3 Applicability of Kinematic and Diffusion Models Ponce,V.M.;Li,R.M.;Simons,D.B.
  15. Ph. D. Dissertation, Cornell University Water Resources Center Synthesis of Hydrographs and Water Surface Profiles for Unsteady Open Channel Flow with Lateral In-flows Ragan,R.M.
  16. Dissertation, Colorado State University The Effect of Moving Rainstorms on Overland Flow Using One-Dimensional Finite Elements Richardson,J.R.
  17. Storm Drainage Res. Proj. Tech. Rep.3 Synthesis of the Inlet Hydrograph Schaake,J.C.,Jr.
  18. Water Resources Research v.18 no.3 A Kinematic Model for Surface Irrigation: An Extension Sherman,B.;Singh,V.P.
  19. Water Resources Research v.19 no.6 A Kinematic Model for Surface Irrigation: Verification by Experimental Data Singh,V.P.;Ram,R.S.