Some efficient Lagrangian mesh finite elements encoded in Zephyr for two-dimensional transport calculations

Using a general finite elements formulation in phase-space and an explicit mesh-by-mesh procedure, the time-independent two-dimensional transport code ZEPHYR provides a good alternative to finite differences production codes DOT and TWOTRAN. This is obtained mainly by two very efficient (stable and accurate) discontinuous finite elements involving triangles and quadrilaterals in R-Z or X-Y space. The accuracy is the same for rectangular grids and for irregular Lagrangian meshes. Comparing with finite differences codes and for a given accuracy the number of meshes may be divided at least by a factor of 4 (awkward geometries are easily tractable with fewer meshes) and the number of iterations may be divided at least by a factor of 2. Moreover the stability of discontinuous finite elements makes fine-mesh rebalance very efficient for convergence acceleration. Thus, for a given accuracy, ZEPHYR's storage requirements may be somewhat larger than DOT's or TWOTRAN's but time requirements may be somewhat smaller. (author)