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Numerical techniques to solve the non-uniform flow of stream water containing one-dimensional advection-dispersion-reaction equation are presented in. At each step, the calculated flow velocity fields of the first model are inputs into the second model. The traditional Crank-Nicolson method is used in the hydrodynamic model. This gives the pollutant concentration field. This provides the velocity field and the water elevation.
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There are two mathematical models used to simulate water quality in non-uniform water flow systems. Among these numerical techniques, finite difference methods, including both explicit and implicit schemes, are mostly used for one-dimensional domains, such as longitudinal stream systems. In, and, the hydrodynamic model and the advection-dispersion equation are used to approximate the velocity of the water current in a bay, uniform reservoir and stream, respectively. A hydrodynamic model provides the velocity field and tidal elevation of the water. The non-uniform flow model requires the velocity of the current at any point and any time in the domain. Numerical techniques for solving the uniform flow of a stream water quality model, especially the one-dimensional advection-dispersion-reaction equation, are presented in, and. In, a finite element method for solving a steady water pollution control to achieve a minimum cost is used. Numerous numerical techniques for solving such models are available. The one-dimensional shallow water equation and the advection-dispersion-reaction equation govern the first and the second models, respectively.
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In water quality modeling for a non-uniform flow stream, the governing equations used are the hydrodynamic model and the dispersion model. This is rather difficult and complex, and the results obtained deviate in measurement from one point in each time/place to another when the water flow in the stream is not uniform. The pollution levels in a stream can be measured via data collection.