S 2 synthetic acceleration and positivity-preserving schemes for solving the neutron transport equation

For the numerical solution of neutron transport equations, both the positivity -preserving property and speeding up the iterative convergence are important and challenging issues. In this work, the combination of the S 2 synthetic acceleration method and a positivity -preserving scheme are derived and analyzed. For the neutron transport and the S 2 equations, we discretize them by the linear discontinuous differencing scheme and apply linear scaling limiter to obtain the non -negative solution. The limiter is simple to implement. Numerical results for solving optically thick problems verify the efficiency of the proposed schemes.