118 research outputs found
A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
Recent work by McClarren & Hauck [29] suggests that the filtered spherical
harmonics method represents an efficient, robust, and accurate method for
radiation transport, at least in the two-dimensional (2D) case. We extend their
work to the three-dimensional (3D) case and find that all of the advantages of
the filtering approach identified in 2D are present also in the 3D case. We
reformulate the filter operation in a way that is independent of the timestep
and of the spatial discretization. We also explore different second- and
fourth-order filters and find that the second-order ones yield significantly
better results. Overall, our findings suggest that the filtered spherical
harmonics approach represents a very promising method for 3D radiation
transport calculations.Comment: 29 pages, 13 figures. Version matching the one in Journal of
Computational Physic
A sweep-based low-rank method for the discrete ordinate transport equation
The dynamical low-rank (DLR) approximation is an efficient technique to
approximate the solution to matrix differential equations. Recently, the DLR
method was applied to radiation transport calculations to reduce memory
requirements and computational costs. This work extends the low-rank scheme for
the time-dependent radiation transport equation in 2-D and 3-D Cartesian
geometries with discrete ordinates discretization in angle (SN method). The
reduced system that evolves on a low-rank manifold is constructed via an
unconventional basis update and Galerkin integrator to avoid a substep that is
backward in time, which could be unstable for dissipative problems. The
resulting system preserves the information on angular direction by applying
separate low-rank decompositions in each octant where angular intensity has the
same sign as the direction cosines. Then, transport sweeps and source iteration
can efficiently solve this low-rank-SN system. The numerical results in 2-D and
3-D Cartesian geometries demonstrate that the low-rank solution requires less
memory and computational time than solving the full rank equations using
transport sweeps without losing accuracy
Uncertainty benchmarks for time-dependent transport problems
Uncertainty quantification results are presented for a well known
verification solution, the time dependent transport infinite plane pulse. The
method of polynomial chaos expansions (PCE) is employed for quick and accurate
calculation of the quantities of interest. Also, the method of uncollided
solutions is used in this problem to treat part of the uncertainty calculation
analytically
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