Numerical models to forecast water quality

The depth-averaged hydrodynamic equations were numerically investigated. Numerical solutions of the equations were obtained using Chebyshev polynomials for a given number of operations and various ratios of the number of layers and the number of polynomials. Numerical solutions were compared with analytical ones using, as an example, the heat conduction equation. The performed numerical studies demonstrated the tendency of the numerical solution to the exact one over time in all cases considered. The best ratio of the number of layers and the number of polynomials was revealed. Comparison of finite-difference solutions with the analytical one for the same number of operations showed the advantage of the polynomial method.