P1 Synthetic Acceleration Scheme for Transport Equation in Two-Dimensional Geometries, Compatible with the Weighted Diamond Differencing Scheme

The P1 synthetic acceleration (P1SA) scheme, compatible with the weighted dia-mond differencing (WDD) scheme for transport equation in two-dimensional (r,z) geometry is developed. A suitable algorithm for solving of the P1SA system for acceleration corrections, based on using of the cyclic alternating direction implicit (ADI) method and the forward-backward substitution method for solving auxiliary two-point systems for corrections in r and z directions is presented. This algorithm doesn't impose any restriction on the choice of the weighting coefficients of the WDD scheme and can be used together, for example, the adaptive WDD (AWDD) scheme. The influence of the length of the ADI cycle and the ADI iterations convergence criterion on the performance of algorithm is tested. Numerical examples of using of the P1SA scheme for solving typical transport problems in (x,z) and (r,z) geometries, including higly-anisotropical ones, are given.