An Extended Slice Balance Approach for Solving the Discrete Ordinates Neutral Particle Transport Equations on the Next Generation of Super-Computers

The research presented in this document extends the slice balance approach (SBA) for solving the discrete ordinates neutral particle transport equations. The extended slice balance approach (ESBA) formulated here improves the accuracy of the underlying spatial discretization scheme in the presence of shadow-type discontinuities by exploiting the new concept of a sub-slice. This research also derives and employs the linear discontinuous nite element (LDFE) spatial discretization scheme within the ESBA framework. Current codes utilizing the SBA rely on low-accuracy discretization schemes, because the geometric information required for higher accuracy schemes has been seen as too voluminous to store and too computationally expensive to re-calculate each time it is needed. Here we show that the judicious use of modern hardware such as the graphics processing unit (GPU) can speed the re-calculation of geometric quantities by factors of a few hundred compared to a single core, raising the possibility that more accurate SBA and ESBA methods may become practical if such hardware is employed. The re-de nition of a slice such that no slice may straddle any arbitrarily placed cut plane parallel to the discrete ordinate, leads to the region in between adjacent cut planes being completely independent of any other such region during a transport \sweep." This provides the ability to divide the mesh into independent regions, resulting in consequences that lead to two new parallel sweep strategies introduced in this document. When considering the LDFE discretization scheme, the ESBA is found to reduce the absolute error for smooth solutions and increase the convergence rate for discontinuous solutions compared to the SBA, which similarly reduces the error and increases the convergence rate over the traditional cell balance approach (CBA). The two parallelization strategies made possible by the ESBA exhibit weak-scaling results similar to those obtained with a simple volume-decomposed parallel transport sweep for both the SBA and CBA. The acceleration of the slice and sub-slice formation process using GPUs is found to exhibit speedups of up to 400 times when compared to a single core of the host CPU