A study of meshless methods for optimization of cathodic protection systems

Abstract Over the last decades, several computer codes have been developed aiming at the full 3D simulation of cathodic protection (CP) systems. CP is a technique applied to prevent corrosive processes and the main goal of the simulation has been to predict the degree of corrosion control achieved. Many pioneering works allowed for the successful application of the boundary element method (BEM) to CP systems. The aim of the present contribution is to introduce a brief overview of cathodic protection system modelling, including some numerical simulations. Mathematical formulations for the electrochemical potential problem are proposed, considering the following meshless methods: the method of fundamental solutions (MFS) and a meshless local Petrov-Galerkin (MLPG2) procedure. The meshless methods performances are evaluated comparing their results with a direct BEM solution procedure. The meshless applications are original first time attempts of such formulations to corrosion problems and cover a lot of practical situations found in actual cathodic protection applications.

[1]  W. J. Santos,et al.  Using the Gaussian function to simulate constant potential anodes in multiobjective optimization of cathodic protection systems , 2016 .

[2]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[3]  J. Telles,et al.  A meshless Reissner plate bending procedure using local radial point interpolation with an efficient integration scheme , 2019, Engineering Analysis with Boundary Elements.

[4]  P. W. Partridge,et al.  The dual reciprocity boundary element method , 1991 .

[5]  W. Tao,et al.  An analysis of the convection–diffusion problems using meshless and meshbased methods , 2012 .

[6]  R. Mathon,et al.  The Approximate Solution of Elliptic Boundary-Value Problems by Fundamental Solutions , 1977 .

[7]  Non‐linear heat conduction in composite bodies: A boundary element formulation , 1988 .

[8]  W. J. Santos,et al.  A new solution technique for cathodic protection systems with homogeneous region by the boundary element method , 2018, European Journal of Computational Mechanics.

[9]  A. Cheng,et al.  Heritage and early history of the boundary element method , 2005 .

[10]  Pihua Wen,et al.  Meshless local Petrov–Galerkin (MLPG) method for wave propagation in 3D poroelastic solids , 2010 .

[11]  J.A.F. Santiago,et al.  Optimal positioning of anodes and virtual sources in the design of cathodic protection systems using the method of fundamental solutions , 2014 .

[12]  L. C. Wrobel,et al.  Optimization of Cathodic Protection Systems Using Boundary Elements and Genetic Algorithms , 2002 .

[13]  P. Doig,et al.  A Finite Difference Numerical Analysis of Galvanic Corrosion for Semi‐Infinite Linear Coplanar Electrodes , 1979 .

[14]  J. Genesca,et al.  Mathematical simulation of a cathodic protection system by finite element method , 2005 .

[15]  ON BOUNDARY ELEMENTS FOR SIMULATION OF CATHODIC PROTECTION SYSTEMS WITH DYNAMIC POLARIZATION CURVES , 1997 .

[16]  J.A.F. Santiago,et al.  An Application of Genetic Algorithms and the Method of Fundamental Solutions to Simulate Cathodic Protection Systems , 2012 .

[17]  Luiz C. Wrobel,et al.  NUMERICAL SIMULATION OF A CATHODICALLY PROTECTED SEMISUBMERSIBLE PLATFORM USING THE PROCAT SYSTEM , 1990 .

[18]  Carlos Alberto Brebbia.  The birth of the boundary element method from conception to application , 2017 .

[19]  J.A.F. Santiago,et al.  An iterative coupling between meshless methods to solve embedded crack problems , 2015 .

[20]  Carlos Alberto Brebbia,et al.  The Boundary Element Method for Engineers , 1978 .

[21]  S. Atluri,et al.  The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods , 2002 .

[22]  Jae-Yong Lim,et al.  Optimizing the sacrificial anode cathodic protection of the rail canal structure in seawater using the boundary element method , 2017 .

[23]  Volkan Cicek.  Cathodic Protection: Industrial Solutions for Protecting Against Corrosion , 2013 .

[24]  W. J. Santos,et al.  An Efficient Hybrid Implementation of MLPG Method , 2017 .