Calculation of the Primary Current Distribution in Cells with Curved Electrodes Using the Finite Difference, Conservative Scheme, and Finite Element Methods

The primary current distribution was calculated in cells with a curvilinear shape of the electrodes by the finite difference (FDM), the conservative scheme (CS), and the finite element methods (FEM). These methods were used for the solutions of the Laplace equation (LE) for a 2D cross-section of a cell consisting of two concentric cylinders (tubes) as electrodes and the inter-electrode space filled with electrolyte. For this cell the analytical solution of LE is known. The local current density on the approximated shape of the electrodes was calculated. The error in the normalized local current density relative to the mean was 5.2%, 52% or 0.2% with FDM using a 64 o 64 mesh, CS using 64 o 64 mesh or FEM using 969 nodes, respectively. Also the boundary element method (BEM) has been used. With 199 elements at the electrode the error in the normalized current density was 0.2%. Taking into account the simplicity of programming and the possibility of using previously developed modules in other calculations, FEM and BEM showed the best performance.