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Numerical simulation based on a combination of finite-element method and proper orthogonal decomposition to prevent the groundwater contamination

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Abstract

In this paper, the coupled advection-dominated diffusion-reaction equations which arise in the prevention of groundwater contamination problem are approximated by usual finite element method (FEM). It is clear that by increasing the number of elements to improve computational accuracy, we have to incur a lot of costs. The main presented idea is to reduce the used CPU time for employing the finite-element method by combining that with a technique which reduces the dimension of the problem. To this end, we apply the proper orthogonal decomposition (POD) technique to the usual FEM for the prevention of groundwater contamination problem to reduce CPU time with acceptable accuracy. Numerical examples are provided to illustrate efficiency and validity of the proposed method.

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Acknowledgements

The authors thank the reviewers for their constructive comments and suggestions that improved the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran

    Mehdi Dehghan, Baharak Hooshyarfarzin & Mostafa Abbaszadeh

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  1. Mehdi Dehghan
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  2. Baharak Hooshyarfarzin
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  3. Mostafa Abbaszadeh
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Correspondence to Mehdi Dehghan.

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Dehghan, M., Hooshyarfarzin, B. & Abbaszadeh, M. Numerical simulation based on a combination of finite-element method and proper orthogonal decomposition to prevent the groundwater contamination. Engineering with Computers 38 (Suppl 4), 3445–3461 (2022). https://doi.org/10.1007/s00366-021-01439-y

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