Volume 13, Issue 1
Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations

Yujing YuanDong Liang

Adv. Appl. Math. Mech., 13 (2021), pp. 1-17.

Published online: 2020-10

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  • Abstract

In this paper, we consider the optimization problem of identifying the pollution sources of convection-diffusion-reaction equations in a groundwater process. The optimization model is subject to a convection-diffusion-reaction equation with pumping point and pollution point sources. We develop a linked optimization and simulation approach combining with the Differential Evolution (DE) optimization algorithm to identify the pumping and injection rates from the data at the observation points. Numerical experiments are taken with injections of constant rates and time-dependent variable rates at source points. The problem with one pumping point and two pollution source points is also studied. Numerical results show that the proposed method is efficient. The developed optimized identification approach can be extended to high-dimensional and more complex problems.

  • Keywords

Convection-diffusion-reaction equation, optimization of identification, pumping point, pollution source point, DE algorithm.

  • AMS Subject Headings

35Q93, 65M32

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yyjyuan@haut.edu.cn (Yujing Yuan)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-13-1, author = {Yuan , Yujing and Liang , Dong}, title = {Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {1}, pages = {1--17}, abstract = {

In this paper, we consider the optimization problem of identifying the pollution sources of convection-diffusion-reaction equations in a groundwater process. The optimization model is subject to a convection-diffusion-reaction equation with pumping point and pollution point sources. We develop a linked optimization and simulation approach combining with the Differential Evolution (DE) optimization algorithm to identify the pumping and injection rates from the data at the observation points. Numerical experiments are taken with injections of constant rates and time-dependent variable rates at source points. The problem with one pumping point and two pollution source points is also studied. Numerical results show that the proposed method is efficient. The developed optimized identification approach can be extended to high-dimensional and more complex problems.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0121}, url = {http://global-sci.org/intro/article_detail/aamm/18337.html} }
TY - JOUR T1 - Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations AU - Yuan , Yujing AU - Liang , Dong JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 1 EP - 17 PY - 2020 DA - 2020/10 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2019-0121 UR - https://global-sci.org/intro/article_detail/aamm/18337.html KW - Convection-diffusion-reaction equation, optimization of identification, pumping point, pollution source point, DE algorithm. AB -

In this paper, we consider the optimization problem of identifying the pollution sources of convection-diffusion-reaction equations in a groundwater process. The optimization model is subject to a convection-diffusion-reaction equation with pumping point and pollution point sources. We develop a linked optimization and simulation approach combining with the Differential Evolution (DE) optimization algorithm to identify the pumping and injection rates from the data at the observation points. Numerical experiments are taken with injections of constant rates and time-dependent variable rates at source points. The problem with one pumping point and two pollution source points is also studied. Numerical results show that the proposed method is efficient. The developed optimized identification approach can be extended to high-dimensional and more complex problems.

Yujing Yuan & Dong Liang. (2020). Optimization of Identifying Point Pollution Sources for the Convection-Diffusion-Reaction Equations. Advances in Applied Mathematics and Mechanics. 13 (1). 1-17. doi:10.4208/aamm.OA-2019-0121
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