A natural coordinate system for calculating neutral particle propagation in the atmosphere due to point sources is two-dimensional spherical-polar coordinates. Deterministic methods for solving the transport equation in this coordinate system require some interesting implementation details stemming from the two angular derivatives present in this form of the equation. In this dissertation, we present a bilinear discontinuous spatial discretization of the transport equation in this coordinate system. The weighted diamond difference discretization is applied to the angular derivative term in two angular dimensions, using zero-weighted starting directions to start the differencing. To our knowledge, the only previous deterministic code that solved the transport equation in the spherical-polar coordinate system was written more than 50 years ago; the development of the deterministic methods we present here and the application to atmospheric transport is new. Numerical experiments are shown to verify that method has better than second-order accuracy and correctly solves the spherical-polar form of the transport equation.
multi-dimensional orthogonal curvilinear discontinuous method, discret ordinates, neutron transport, atmospheric transport
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Wakeford, Daniel T.. "A Two-Dimensional Spherical-Polar Multigroup Discrete Ordinates Code for Atmospheric Particle Transport." (2020). https://digitalrepository.unm.edu/ne_etds/97