Geodesic
Modelling of electric fields in axisymmetric systems for cathode protection of underground structures
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 3, pp. 161-169 Cet article a éte moissonné depuis la source Math-Net.Ru

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The aim of this work is to carry out numerical calculation of electric fields in axisymmetric systems for cathode protection of underground structures against corrosion. As is known, cathode protection is a complex multi-parameter system, which has a number of features depending on the type and form of the protected structure, properties of the surrounding environment, etc. As a result, the modelling of protection parameters is quite complex and requires new more advanced computer technologies. In this work, we construct a mathematical model of the problem on the electric field distribution in an axisymmetric system for cathode electrochemical protection of underground structures. In addition, we propose an algorithm to solve the problem. The algorithm is based on the use of integral Green transformations and, in particular, the second Green integral formula. Also, we give an example of a computer implementation of the proposed algorithm in the case of a homogeneous half-space. The Scilab application package is used to implement the example.
Keywords: mathematical modelling, cathodic protection, electric field, Green integral formula, Scilab. 
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Т. М. Shamsutdinova. Modelling of electric fields in axisymmetric systems for cathode protection of underground structures. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 3, pp. 161-169. http://geodesic.mathdoc.fr/item/VYURU_2019_12_3_a13/

[1] Taylor C. D., “Corrosion Informatics: An Integrated Approach to Modelling Corrosion”, Corrosion Engineering, Science and Technology, 50:7 (2015), 490–508 | DOI

[2] Hameed K. W., Yaro A. S., Khadom A. A., “Mathematical Model for Cathodic Protection in a Steel-Saline Water System”, Journal of Taibah University for Science, 10:1 (2016), 64–69 | DOI

[3] Bolotnov A. M., Bashaev M. A., Hisametdinov F. Z., “Interval Calculations in the Algorithms for Calculating the Electric Fields of Cathodic Protection of Main Pipelines”, Management Systems and Information Technology, 62:4 (2015), 71–74 (in Russian)

[4] Dmitriev V. I., “The General Method of Calculating the Electromagnetic Field in a Layered Medium”, Computational Methods and Programming, 1968, no. 10, 55–65 (in Russian)

[5] Ostapenko V. N., Lukovich V. V., Kolesnik T. V., Kohanovskij I. N., Methods for Calculating the Cathodic Protection of Metal Structures against Corrosion, Naukova Dumka, Kiev, 1966 (in Russian)

[6] Tihonov A. N., Samarskii A. A., Equations of Mathematical Physics, Nauka, M., 1977 (in Russian) | MR

[7] Dmitriev V. I., Zaharov E. V., Integral Equations in Boundary Problems of Electrodynamics, MSU, M., 1987 (in Russian)

[8] Ivanov V. T., Yakovleva T. M., “A Method for Calculating the Electric Field in a Cylindrically Layered Medium from a Point Source”, Izvestiya. Physics of the Solid Earth, 33:10 (1997), 859–861

[9] Ivanov V. T., Yakovleva T. M., “Mathematical Modelling of Electric Fields in Electrochemical Protection Systems in Stratified Media”, Russian Journal of Electrochemistry, 32:10 (1996), 1133–1139

[10] Kantorovich L. V., Krylov V. I., Approximate Methods of Higher Analysis, Fizmatgiz, M.–L., 1962 (in Russian) | MR