Cell-centered particle weighting algorithm for PIC simulations in a non-uniform 2D axisymmetric mesh

Standard area weighting methods for particle-in-cell simulations result in systematic errors on particle densities for a non-uniform mesh in cylindrical coordinates. These errors can be significantly reduced by using weighted cell volumes for density calculations. A detailed description on the corrected volume calculations and cell-centered weighting algorithm in a non-uniform mesh is provided. The simple formulas for the corrected volume can be used for any type of quadrilateral and/or triangular mesh in cylindrical coordinates. Density errors arising from the cell-centered weighting algorithm are computed for radial density profiles of uniform, linearly decreasing, and Bessel function in an adaptive Cartesian mesh and an unstructured mesh. For all the density profiles, it is shown that the weighting algorithm provides a significant improvement for density calculations. However, relatively large density errors may persist at outermost cells for monotonically decreasing density profiles. A further analysis has been performed to investigate the effect of the density errors in potential calculations, and it is shown that the error at the outermost cell does not propagate into the potential solution for the density profiles investigated.