Boundary element approach to mass and charge transport in electrochemical cells

A boundary element numerical scheme for the two‐dimensional convection–diffusion equation

“…Applying the weighted residual technique to Equation (5) in the domain ∈ E 2 , the following domain integrals appear…”

“…To apply the BEM it is necessary to transform the differential equation that governs the analysed problem, in this case expression (3), into a boundary integral equation (BIE in the scientific where all the terms not brought together in the second-order differential operator L have been grouped in (x, t). Applying the weighted residual technique to Equation (5) in the domain ∈ E 2 , the following domain integrals appear · L[] dV = · (x, t) dV (6) where is the fundamental solution that verifies the following differential equation:…”

“…The time derivative term */*t will in this case be dealt with by means of a step-by-step integration process, with approximation of the time derivative by means of finite differences, and the resulting terms corresponding to previous instants will be considered as being pseudo-forces in the second member, approximated by means of the DRM. This third option is taken by various authors [5,6,9,[12][13][14][15], and this is the one taken up in the present study. In what follows, the differential operator associated with the convection-diffusion equation will be…”

“…Various numerical methods have been used to solve physical problems governed by this type of equation in the last three decades. A brief look at the scientific publications of the last 30 years shows the boundary elements method (BEM) being applied to a great variety of phenomena governed by this equation, such as those of 2064 L. M. ROMERO AND F. G. BENITEZ a magnetic field generated by a moving conductor [2], convective heat transfer [3], heat transfer in a continuous casting process [4], mass and charge transfer in electrochemical cells [5,6], volumetric transport of surfactant with semi-infinite progression of a bubble in capillary tubes [7], propagation of a contaminant in a fluid medium, etc. The approach of the BEM to the problem of traffic in cities or large towns with dense road networks was first formulated one decade ago [8].…”

Numerical solution of convection-diffusion problems at high Péclet number using boundary elements

“…13 The mathematical model includes the combined e ects of di usion, convection and migration for ions concentrations and electric potential, and is described by a coupled system of non-linear equations. The BEM model rewrites these equations as linear convection-di usion equations with non-linear forcing terms, and solves them iteratively.…”