An implicit-explicit time differencing scheme for neutron transport in moving materials

The use of transport sweeps and implicit time differencing are standard in neutron transport codes. The added complication of advection operators, which result from transforming the equation to the co-moving (material) frame to account for moving material effects, have been dealt with using an operator split with a mixture of time implicit and explicit steps. Here, an implicit-explicit (IMEX) time differencing approach is explored in which the co-moving frame transport equation is solved directly using a modified implicit time differencing scheme in which spatial upwinding terms that appear in the discretization of the streaming and spatial advection operators are lagged at the incoming time edge. Convergence and stability analyses are conducted and the accuracy of the scheme verified using the method of manufactured solutions. (author)