Implementing and Testing Upstream Corner Balance Methods in PDT
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Among the many applications that require solutions of the particle transport equation are nuclear reactors, medical imaging, medical therapy, photon interaction in the atmosphere and oceans, industrial systems, and radiative transfer problems arising from many areas including astrophysics and inertial confinement fusion. For most transport problems of practical interest it is not possible to find analytic solutions. Thus, discrete approximations must be employed. Many spatial discretization methods exist that can provide accurate solutions if the spatial mesh is sufficiently fine, but the computational cost of transport problems would often prohibitively large if such a fine mesh were to be employed. Obtaining an accurate solution on a coarser mesh is significant. Upstream corner balance (UCB) methods are a specific family of spatial discretization methods that have some advantages over other methods. This research assesses the strengths and weaknesses of UCB by implementing, testing, and comparing UCB methods against other spatial discretization methods in the particle transport code PDT. In the test problems simulated, UCB was found to outperform the piecewise linear discontinuous (PWLD) method and the corner balance-step (CB-STEP) method. Based on these encouraging results, this research lays the foundation for further testing and development of UCB methods on a larger scale. With continued research, a robust, accurate, and efficient spatial discretization method could result.
Seager, Robert John (2014). Implementing and Testing Upstream Corner Balance Methods in PDT. Honors and Undergraduate Research. Available electronically from