# 부등류조건에서 종확산방정식의 Eulerian-Lagrangian 모형

• 김대근 (대불대학교 토목환경공학과) ;
• 서일원 (서울대학교 토목공학과)
• Published : 2002.09.01
• 67 9

#### Abstract

Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.

#### Keywords

Eulerian-Lagrangian model;dispersion equation;operator-splitting approach;method of characteristics

#### References

1. Holly, F.M., and J.M. Usseglio-Polatera, 1984, Pollutant dispersion in tidal flow, J. Hyd. Eng. ASCE, 110(7), 905-926. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:7(905)
2. Noye, J., 1987, Numerical methods for solving the transport equation, Numerical Modeling : Application to Marine System, ELSEVIER SCIENCE PUBLISHERS B.V., 195-229. https://doi.org/10.1016/S0304-0208(08)70035-5
3. Seo, I. W. and D. G. Kim, 1994, Numerical modeling of one-dimensional longitudinal dispersion equation using Eulerian-Lagrangian method, J. of Korea Water Resources Association, 27(2) 155-166.
4. Yang, J. E. and E. L. Hsu, 1991, On the use of the reach-back characteristics method for calculation of dispersion, International J. for Numerical Methods in Fluids, 12, 225-235. https://doi.org/10.1002/fld.1650120303
5. Jun, K. S. and K. S. Lee, 1993, An EulerianLagrangian hybrid numerical method for the longitudinal dispersion equation, J. of Korean Association of Hydrological Sciences, 26(3), 137-148.
6. Lee, K. S. and J. W. Kang, 1987, Characteristics of the finite difference approximations for the convective dispersion model, J, of Korean Society of Civil Engineers, 7(4), 147-157.
7. Leonard, B.P., 1979, A stable accurate convective modeling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Eng., 19, 59-98. https://doi.org/10.1016/0045-7825(79)90034-3
8. Baptista, A.E.M., E.E. Adams, and K.D. Stolzenbach, 1984, Eulerian-Lagrangian analysis of pollutant transport in shallow water, Report No. 296, Ralph M. Parsons Laboratory Aquatic Sciences and Environmental Engineering, Department of Civil Engineering, Massachusetts Institute of Technology.
9. Abott, M.B. and D.R. Basco, 1989, Computational fluid dynamics : An introduction for engineers, Longman Scientific & Technical, London.
10. Toda, K., and F.M. Holly, 1986, Hybrid numerical method for linear advection-dispersion, Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa.
11. Jun, K. S. and K. S. Lee, 1994, EulerianLagrangian split-operator method for the longitudinal dispersion equation, J. of Korean Society of Civil Engineers, 14(1), 131-141.
12. Kim, D. G., 1995, Modeling transverse mixing in natural channels, Thesis, Seoul National University, Korea.
13. Holly, F.M., and A. Preissmann, 1977, Accurate calculation of transport in two dimensions, J, Hyd. Div., ASCE, 103(11), 1259-1277.
14. Cheng, R.T., C. Vinenzo, and M. Nevil, 1984, Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates, Water Resources Research, 20(7), 944-952. https://doi.org/10.1029/WR020i007p00944