A piecewise linear discontinuous finite element spatial discretization of the transport equation in 2D cylindrical geometry Conference Paper uri icon

abstract

  • We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method. We conclude that the piecewise linear method extends the excellent performance of linear discontinuous (on triangles) and bilinear discontinuous (on quadrilaterals) to general polygons. This includes "polygons" generated by adding "hanging nodes" to simpler cells, via local refinement, or by "cutting" simpler cells to represent materials interfaces.

published proceedings

  • American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009

author list (cited authors)

  • Bailey, T. S., Adams, M. L., Chang, J. H., & Warsa, J. S.

complete list of authors

  • Bailey, TS||Adams, ML||Chang, JH||Warsa, JS

publication date

  • December 2009