BEM simulation of cathodic protection systems employed in infinite electrolytes.

*(English)*Zbl 0619.65122The authors consider the numerical solution of the problem of cathode protection. The boundary condition for the potential on the cathode is nonlinear, and the authors obtain an integral equation involving the potential over the boundary, for the potential, and also involving the potential at infinity which is unknown. This is discretized using triangular boundary elements and it is stated that the nonlinear equations arising can be solved rapidly by Newton-Raphson iteration. The method is illustrated by two simple examples. The formulation discussed avoids the difficulties associated with the discretization of an infinite domain. It is also possible to find the potential at infinity.

Reviewer: Ll.G.Chambers

##### MSC:

65Z05 | Applications to the sciences |

65R20 | Numerical methods for integral equations |

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

78A55 | Technical applications of optics and electromagnetic theory |

35Q99 | Partial differential equations of mathematical physics and other areas of application |

35C15 | Integral representations of solutions to PDEs |

45G05 | Singular nonlinear integral equations |

PDF
BibTeX
XML
Cite

\textit{N. G. Zamani} et al., Int. J. Numer. Methods Eng. 24, 605--620 (1987; Zbl 0619.65122)

Full Text:
DOI

##### References:

[1] | and , Corrosion Engineering, McGraw-Hill Book Company, 1978. |

[2] | Cathodic Protection, The Macmillan Company, New York, 1960. |

[3] | and , Modern electrochemistry, Plenum Press, New York, 1974. |

[4] | Waber, Journal of The Electrochemical Society 101 pp 271– (1954) |

[5] | Waber, Journal of The Electrochemical Society 102 pp 344– (1955) |

[6] | Waber, Journal of The Electrochemical Society 102 pp 420– (1955) |

[7] | Waber, Journal of The Electrochemical Society 103 pp 64– (1956) |

[8] | Wagner, Journal of The Electrochemical Society 98 pp 116– (1951) |

[9] | Wagner, Journal of The Electrochemical Society 99 pp 1– (1952) |

[10] | Zamani, Int. j. numer. methods eng. 23 pp 1295– (1986) |

[11] | and , ’Numerical simulation of the electroplating phenomenon or reversed corrosion’, Technical Report, CADCAMTR-85-06, Technical University of Nova Scotia, October 1985. |

[12] | and , ’Boundary element method in electroplating problems’, Proceedings of The International Conference on Boundary Element Technology, BETECH 86, Massachusetts Institute of Technology, Cambridge, June 1986. |

[13] | and , ’Current density/voltage calculations using boundary element techniques’, Corrosion 83, paper number 211, 1983. |

[14] | Zamani, Journal of Applied Mathematical Modelling 1 (1986) |

[15] | Integral Equations and Partial Differential Equations, A Course of Higher Mathematics, Vol. IV, Pergamon Press, London, 1964. |

[16] | Green’s Functions and Boundary Value Problems, Wiley, 1979. |

[17] | ’Modelling of electrochemical phenomena for finite element analysis of galvanic systems I-use of applied current (conduction) boundary conditions’, TM. No. 831019, Naval Underwater Systems Center, New London, connecticut, 1983. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.