Unconditional stable numerical techniques for a water-quality model in a non-uniform flow stream

Advances in Difference Equations

Nopparat Pochai¹ 

[1] Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

关键词: Crank-Nicolson scheme;    new fourth-order scheme;    Saulyev scheme;    hydrodynamic model;    dispersion model;    65N06;    65M06;    35L40;    35K57;   

DOI  :  10.1186/s13662-017-1338-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Two mathematical models are used to simulate water quality in a non-uniform flow stream. The first model is the hydrodynamic model that provides the velocity field and the water elevation. The second model is an advection-diffusion-reaction model that provides the pollutant concentration field. Both models are formulated as one-dimensional equations. The traditional Crank-Nicolson method is also used in the hydrodynamic model. At each step, the flow velocity fields calculated from the first model are the inputs into the second model. A new fourth-order scheme and a Saulyev scheme are simultaneously employed in the second model. This paper proposes a remarkably simple alteration to the fourth-order method so as to make it more accurate without any significant loss of computational efficiency. The results obtained indicate that the proposed new fourth-order scheme, coupled to the Saulyev method, does improve the prediction accuracy compared to that of the traditional methods.

【 授权许可】

CC BY