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Free mesh radial basis function collocation approach for the numerical solution of system of multi‐ion electrolytes
Author(s) -
La Rocca A.,
Power H.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1410
Subject(s) - radial basis function , interpolation (computer graphics) , collocation (remote sensing) , basis function , reaction–diffusion system , mathematics , neumann boundary condition , boundary (topology) , numerical analysis , electrolyte , ion , boundary value problem , basis (linear algebra) , mathematical analysis , chemistry , geometry , physics , computer science , electrode , classical mechanics , machine learning , artificial neural network , motion (physics) , organic chemistry
The main objective of this work is to show the versatility of an innovative mesh‐free numerical scheme, which allows the solution of the coupled transport equations governing the evolution of a system of multi‐ion electrolytes, by mean of the use of radial basis functions interpolation and a nesting approach. The nesting approach is used in order to capture the detail behaviour of the solution near a solid wall i.e. at the diffusion–reaction layer. As a numerical example the problem of silver deposition on a rotating disk is analysed. The versatility of the proposed numerical scheme is proved by solving the proposed electrochemical phenomena imposing three different kinds of boundary conditions at the solid wall (Dirichlet, Neumann and Robin). The obtained numerical results are compared with simplified analytical approximation of the corresponding problems. The effect of the ligand concentration on the others species is considered and a comparison between the obtained concentration profiles for the complex AgS 2 O 3 −and Ag(S 2 O 3 ) 2 −3when the concentration of the ligand S 2 O 3 −2takes different values is shown. Copyright © 2005 John Wiley & Sons, Ltd.