Refined Numerical Scheme for Advective Transport in Diffusion Simulation
This article has a reply.
VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 123, Issue 1
Abstract
We propose an accurate numerical scheme for calculating advection in the simulations of mass, heat, and momentum transport. The second-order spatial derivatives of the advection-diffusion equation can be discretized more accurately by the usual finite-difference approximation than the first-order spatial derivatives. By taking this feature into account, we can expect that the second-order wave equation is more available for numerical calculation of pure advection than the first-order advection equation. However, the second-order wave equation has two types of propagating wave solutions, one of which is unnecessary. To get a unique solution that shows the downstream advection only, the concept of characteristics method is applied. By minimizing truncation errors in the scheme, the parameters involved could be determined as functions of the Courant number. Comparison of this scheme with several others in model calculations proves its superior accuracy and stability. The proposed scheme uses only three grid points in space in case of one-dimensional problems. In addition, this can be easily applied to multidimensional practical problems.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, M. B. (1979). Computational hydraulics. Pitman Publishing Ltd., London, England.
2.
Baptista, A. M., Adams, E. E., and Stolzenbach, K. D. (1987). “Comparison of several Eulerian-Lagrangian models to solve the advection-diffusion equation.”Turbulent measurements and flow modeling, C. J. Chen, L. D. Chen, and F. M. Holly Jr., eds., Springer-Verlag, Berlin, Germany, 345–354.
3.
Cunge, J. A., Holly, F. M. Jr., and Verway, A. (1986). Practical aspects of computational river hydraulics. Inst. of Iowa Hydr. Res., Univ. of Iowa, Iowa City, Iowa.
4.
Glass, J., and Rodi, W. (1982). “A higher order numerical scheme for scalar transport.”Computer methods applied mechanics and engineering, 31, North-Holland Publishing Co., Amsterdam, The Netherlands, 337–358.
5.
Holly, F. M. Jr., and Preissmann, A.(1977). “Accurate calculation of transport in two dimensions.”J. Hydr. Div., ASCE, 103(11), 1259–1277.
6.
Holly, F. M. Jr., and Usseglio-Polatera, J. M.(1984). “Dispersion simulation in two-dimensional tidal flow.”J. Hydr. Engrg., ASCE, 110(7), 905–926.
7.
Komatsu, T., Holly, F. M. Jr., Nakashiki, N., and Ohgushi, K.(1985). “Numerical calculation of pollutant transport in one and two dimensions.”J. Hydrosci. and Hydr. Engrg., Tokyo, Japan, 3(2), 15–30.
8.
Komatsu, T., Ohgushi, K., Asai, K., and Holly, F. M. Jr.(1989). “Accurate numerical simulation of scalar advective transport.”J. Hydrosci. and Hydr. Engrg., 7(1), 63–73.
9.
Ohno, Y., and Isoda, K. (1990). Handbook of numerical calculation. Ohmu-sha, Japan (in Japanese).
10.
Tamamidis, P., and Assanis, D. N.(1993). “Evaluation of various high-order-accuracy schemes with and without flux limiters.”Int. J. Numer. Methods Fluids, 16, 931–948.
11.
Yananko, N. N. (1968). Methode a Pas Fractionnaires, P. A. Nepomiastchy, translator, Armand Colin, Paris, France (in French).
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 1 • January 1997
Pages: 41 - 50
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Jan 1, 1997
Published in print: Jan 1997
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.