A Block Adaptive Mesh Refinement Algorithm for the Neutral Particle Transport Equation

Abstract

We describe the development and implementation of a block-based adaptive mesh refinement (AMR) algorithm for solving the discrete ordinates neutral particle transport equation. AMR algorithms allow mesh refinement in areas of interest without requiring the extension of this refinement throughout the entire problem geometry, minimizing the number of computational cells required for calculations. The block-based AMR algorithm described here is a hybrid between traditional cell or patch-based approaches and is designed to allow an efficient parallel solution of the transport equation while still reducing the cell count.This paper discusses the data structure implementation and CPU/memory efficiency for our Block AMR method, the equations and procedures used in mapping edge fluxes between blocks of different refinement levels for both diamond and linear discontinuous spatial discretizations, effects of AMR on mesh convergence, and our approach to parallelization. Comparisons between our Block AMR method and a traditional single-level mesh are presented for a sample brachytherapy problem. The Block AMR results are shown to be significantly faster for this problem (on at least a few processors), while still returning an accurate solution.