Solving of multigroup non-stationary transport equation in axial r-z geometry on grids formed by the arbitrary convex quadrangles

The numerical method for solving the multigroup non-stationary transport equation is developed in two-dimensional axial R-Z geometry on grids formed by arbitrary convex quadrangles. The semi-implicit algorithm for solving the system of non-stationary equations is developed. The conservative finite-difference scheme is obtained by the integro-interpolated method. The balance equation is augmented by linear approximations. The proposed additional relationships provide the second order of approximation at any side-visible cases under the correspondent choice of the weights of scheme. Number of additional relationships over spatial variables and their form are determined depending on one, two or three side-visible cases. The additional relationships over the time and angle variables are diamond-difference-like approximations relating the edge values to the cell-centered values. Testing of the algorithm for solving the stationary transport equation is based on the comparison of the numerical results obtained by the developed technique with the results obtained by the 1D codes KIN1D (KIAM, Russia) and ANISN (USA) by using the spherical symmetrical one-dimensional problems. The special analytical Benchmarks are developed for testing the non-stationary technique. The testing has shown the good coincidence of the results. (author)