## Numerical simulation of a one-dimensional water-quality model in a stream using a Saulyev technique with quadratic interpolated initial-boundary conditions.(English)Zbl 1470.76069

Summary: The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems such as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform, then numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the one-dimensional water-quality model in a stream is proposed. The governing equation is advection-diffusion-reaction equation with nonuniform boundary condition functions. The approximated pollutant concentrations are obtained by a Saulyev finite difference technique. The boundary condition functions due to nonuniform pollutant concentrations at the discharge point are defined by the quadratic interpolation technique. The approximated solutions to the model are verified by a comparison with the analytical solution. The proposed numerical technique worked very well to give dependable and accurate solutions to these kinds of several real-world applications.

### MSC:

 76M20 Finite difference methods applied to problems in fluid mechanics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs

SHASTA
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### References:

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