A two Dimensional Numerical Model for Mixing in Natural Rivers
Numerous numerical models have been developed for convection-diffusion processes in river channels based on either finite difference or finite element methods. Any two-dimensional dispersion model requires a hydrodynamic model to provide a description of the velocity field. For the case of mixing in natural rivers, two-dimensional potential flow solutions are often used. Potential flow solutions are not able to provide an adequate description of the velocity field in rivers where the effect of transverse depth variations is important. Numerical simulations of the flow field in a river, taking into account the depth variations, is very cumbersome if not impractical. Recently, Yotsukura and Sayre (1976) have shown that by employing the concept of stream-tube and orthogonal curvilinear coordinate system, a simple form of convection-diffusion equation can be obtained for steady state two-dimensional mixing in meandering rivers. This formulation was extended to the case of transient mixing by Shen (1978). This type of formulation eliminates the presence of the transverse velocity term in the convection-diffusion equation and maps the irregular physical domain into a rectangular strip in the new coordinate system thereby simplifying the problem for numerical simulation. This model also has the advantage of avoiding the difficulties in simulating the flow field numerically by using simple simulation formulas for transverse flow distributions.
KeywordsCollocation Method Natural River Cumulative Discharge Local Truncation Error Natural Coordinate System
Unable to display preview. Download preview PDF.
- Curtis, A.R. and Reid, J.K. (1971) The Solution of Large Sparse Unsymmetric Systems of Linear Equations, Information Processing, 71:1240–1245.Google Scholar
- Eisental, S.C., Schultz, M.H. and Sherman, A.H. (1975) Considerations in the Design of Software for Sparse Gaussian Elimination, Proc. Symp. on Sparse Matrix Computations, Argonne National Laboratory, 263–273.Google Scholar
- Harden, O.T., Shen, H.T. (1979) Numerical Simulation of Mixing in Natural Rivers, Jour. Hydr. Div., ASCE, 105, HY4:393–408.Google Scholar
- Shen, H.T. (1978) Transient Mixing in River Channels, Jour. Environ. Eng. Div., ASCE, 104, EE2:445–459.Google Scholar
- Shen, H.T., Ackermann, N.L. (1980) Wintertime Flow Distribution in River Channels, Jour. Hydr. Div., ASCE, 106, HY5:805–817.Google Scholar
- Sherman, A.H. (1978) Algorithms of Sparse Gaussian Elimination with Partial Pivoting, ACM Trans. Math. Software, 4, 4:440–338.Google Scholar
- Yotsukura, N. and Cobb, E.D. (1972) Transverse Diffusion of Solutes in Natural Streams, U.S.G.S. Prof. Paper, 582-C.Google Scholar
- Yotsukura, N., Fischer, H.B. and Sayre, W.W. (1970) Measurements of Mixing Characteristics of the Missouri River Between Sioux City, Iowa and Plattsmouth, Nebraska, U.S.G.S. Water-Supply Paper, 1899-G.Google Scholar