Water for future (물과 미래)

Korea Water Resources Association (한국수자원학회)
권호 표지

Markov Chain Model for Synthetic Generation by Classification of Daily Precipitaion Amount into Multi-State

강수계열의 상태분류에 의한 Markov 연쇄 모의발생모형

  • 김주환 (한국수자원공사 수자원연구소) ;
  • 박찬영 (인하공업전문대학 토목과)
  • Published : 1996.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

A finite element model for simulating gradually and rapidly varied unsteady flow in open channel is developed based on dynamic wave equation using Petrov-Galerkin method. A matrix stability analysis shows the selective damping of short wave lengths and excellent phase accuracies achived by Petrov-Galerkin method. Whereas the Preissmann scheme displays less selective damping and poor phase accuracies, and Bubnov-Galerkin method shows nondissipative characteristics whicn causes a divergence problem in short wave length. The analysis also shows that the Petrov-Galerkin method displays the desirable combination of selective damping of high frequency progressive waves over a wide range of Courant number and good phase accuracy at low Courant number. Therefore, the Petrov-Galerkin can be effectively applied to gradually and rapidly varied unsteady flow.

개수로내의 검변 및 급변 부정류 해석을 위해서 dynamic wave식을 기본방정식으로 하고 이를 불연속 보간함수와 upstream weighting 을 도입한 Petrov-Galerkin 기법에 의해 해석하는 유한요소모형을 개발하였다. 매트릭스 안정성 해석 결과 Petrov-Galerkin기법은 단파장에서의 선택적 감쇠능력과 위상오차에 있어 우수한 것으로 나타났다. 반면에 Preissmann기법은 단파장에서의 선택적 감쇠능력과 위상오차에 있어 열등한 것으로 나타났고, Bubnov-Galerkin 기법은 비감쇠특성을 나타내고 있어 단파장 영역에서 발산해를 일으키는 주요원인임을 확인할 수 있었다. Petrov-Galerkin 방법은 Courant수의 넓은 범위에서 높은 주파수를 가진 진행파에 대한 선택적인 감쇠와 작은 Courant 수의 범위에서 양호한 위상정도를 가지는 이상적인 조합을 나타내고 있어 점변 및 급변 부정류 해석에 있어 이상적인 기법으로 활용될 수 있을 것으로 판단되었다.

Keywords

References

  1. 한국수자원학회지 v.27 no.2 개수로에서의 상류-사류 천이영역에 대한 부정류 해석 한건연;박재홍;이종태
  2. Computational fluid dynamics Abbott, M.B.;Basco, D.R.
  3. Comput. Methods in App. Mech. Eng. v.27 On the accuracy and efficiency of a finite element tensor product algorithm for fluid dynamics applications Baker, A.J.;Soliman, M.O.
  4. Comput. Methods. App. Mech. Eng. v.32 Streamline upwind / Petrov - Galerkin formualtions for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Brooks, A.N.;Hughes, T.J.R.
  5. J. of Hydr. Div. v.102 no.HY6 finite element solution of Saint-Venant equations Cooley, R.L.;Moin, S.A.
  6. SIAM J. of Num. Anal. v.11 Two methods of Galerkintype achieving optimum L² rates of convergence for first-order hyperbolics Dendy, J.E.
  7. SIAM J. of Num. Anal. v.10 Galerkin methods for first-order hyperbolics: An example Dupont, T.
  8. Finite elements in water resources Ⅲ Do finite element models simulate surface flow ? Gray, W.G.;S.Y. Wang(et al.)(eds.)
  9. Advances in Water Resources v.1 no.2 Time stepping schemes for finite element tidal model computations Gray, W.G.;Lynch, D.R.
  10. J. of Hydr. Eng. v.110 no.4 A dissipative Galerkin scheme for open-channel flow Katopodes, N.D.
  11. J. of Hydr. Div. v.102 no.HY4 Application of finite element method to open channel flow Keuning, D.H.
  12. Finite elements in water resources Finite element models for unsteady flow routing through irregular channels King, I.P.;C.A. Brebbia(et al.)(eds.)
  13. Proc. of the 4th International Conference on Finite Elements in Water Resources Time-weighting of the momentum equation in explicit wave-equation models of surface water flow Kinnmark, I.P.;Gray, W.G.
  14. Computer modeling of free-surface and pressurized flow Upwinding and characteristics in FD and FE methods Malcherek, A.;Zielke, W.;M.H. Chaudhry(ed.);L.W. Mays(ed.)
  15. Monthly Weather Review v.104 no.12 Selective damping in a galerkin method for solving wave problems with variable grids Raymond, W.H.;Garder, A.