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A Non-Hydrostatic Pressure Model and its Implementation of the Dynamic Boundary Condition

동수압 모형의 동역학적 경계조건

  • Received : 2008.07.21
  • Accepted : 2008.10.04
  • Published : 2008.11.30

Abstract

In this paper, a three-dimensional non-hydrostatic pressure model for free surface flows using a normalized vertical coordinate system is presented. To strongly couple the free surface and non-hydrostatic pressure in the momentum equations, a double predictor-corrector method is employed. This research is especially focused on implementing the dynamic boundary condition (a zero pressure condition) at the free surface. This boundary condition can be specified accurately with a small modification to existing models. Numerical results with and without this modification clearly show that a precise implementation of the dynamic boundary condition is paramountly important.

본 연구에서는 자유수면 흐름에 적용할 수 있는 연직방향에 대해 좌표변환된 3차원 동수압 모형을 제시하였다. 제시한 모형은 자유수면과 동수압의 해석을 위하여, 2중 예측-수정(double predictor-corrector)방법을 적용하였다. 본 연구에서는 정확한 동역학적 경계조건(자유수면에서의 압력은 0인 조건)을 적용하는 방법을 검토하였고, 이 경계조건은 기존에 개발된 모형에 미소한 수정을 통하여 적용 가능함을 보여주었다. 본 연구에서 제시한 모형과 기존 모형의 계산결과를 비교하였을 때 동역학적 경계조건의 정확한 적용이 매우 중요함을 알 수 있다.

Keywords

References

  1. Beji, S. and Battjes, J.A. (1993) Experimental investigation of wave propagation over a bar. Coastal Eng., Vol. 19, No. 1-2, pp. 151-162. https://doi.org/10.1016/0378-3839(93)90022-Z
  2. Casulli, V. (1999) A semi-implicit finite difference method for nonhydrostatic, free-surface flows, Int. J. Numer. Meth., Fluids., Vol. 30, pp. 425-440. https://doi.org/10.1002/(SICI)1097-0363(19990630)30:4<425::AID-FLD847>3.0.CO;2-D
  3. Casulli, V. and Cattani, E. (1994) Stability accuracy and efficiency of a semi-implicit method fro three-dimensional shallow water flow, Comput. Math. Appl., Vol. 27, No. 4, pp. 99-112.
  4. Casulli, V. and Zanolli, P. (2002) Semi-implicit numerical modelling of nonhydrostatic free-surface flows for environmental problems, Math. Comp. Modeling., Vol. 36, No. 9-10, pp. 1131-1149. https://doi.org/10.1016/S0895-7177(02)00264-9
  5. Chen, X. (2003) A free-surface correction method for simulating shallow water flows, J. Comput. Phys., Vol. 189, pp. 557-578. https://doi.org/10.1016/S0021-9991(03)00234-1
  6. Lee, J.W., Teubner, M.D., Nixon J.B., and Gill, P.M. (2006) A 3-D non-hydrostatic model for small amplitude free surface flows, Int. J. Numer. Meth. Fluids., Vol. 50, pp. 649-672. https://doi.org/10.1002/fld.1054
  7. Li, B. and Fleming, C.A. (2001) Three-dimensional model of Navier-Stokes equations for water waves, J. Waterway. Port Coast. Ocean Eng., Vol. 127, pp. 16-25. https://doi.org/10.1061/(ASCE)0733-950X(2001)127:1(16)
  8. Lin, P. and Li, C.W. (2002) A s-coordinate three-dimensional numerical model for surface wave propagation, Int. J. Numer. Meth. Fluids., Vol. 38, pp.1045-1068. https://doi.org/10.1002/fld.258
  9. Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow, Hemisphere Pub.
  10. Phillips, N.A. (1957) A coordinate system having some special advantages or numerical forecasting. J. Meteor., Vol. 14, pp. 184-185. https://doi.org/10.1175/1520-0469(1957)014<0184:ACSHSS>2.0.CO;2
  11. Saad, Y. (1992) Numerical methods for large eigenvalue problems (Algorithms and architectures for advanced scientific computing), John Wiley and Sons Inc.
  12. Shi, J. and Toro, E.F. (1996) Fully discrete high-order shock-capturing numerical schemes, Int. J. Numer. Meth. Fluids., Vol. 23, pp. 241-269. https://doi.org/10.1002/(SICI)1097-0363(19960815)23:3<241::AID-FLD421>3.0.CO;2-L
  13. Stelling, G.S. and Zijlema, M. (2003) An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation, Int. J. Numer. Meth. Fluids., Vol. 43, pp. 1-23. https://doi.org/10.1002/fld.595
  14. Van der Vorst, H.A. (1992) BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., Vol. 13, pp. 631-644. https://doi.org/10.1137/0913035
  15. Vreugdenhil, C.B. (1994) Numerical methods for shallow-water flow, Kluwer Academic Publishers.
  16. Yuan, H. and Wu, C.H. (2004) An implicit three-dimensional fully non-hydrostatic model for free-surface flows, Int. J. Numer. Meth. Fluids., Vol. 46, pp. 709-733. https://doi.org/10.1002/fld.778