A low-rank method for two-dimensional time-dependent radiation transport calculations

•A low-rank scheme of the radiation transport equation is developed.•The time evolution of the radiation intensity is constrained in low-rank manifolds.•Computational cost and memory are significantly reduced without sacrificing accuracy.•A major improvement in accuracy can be obtained by a slight i...

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Bibliographic Details
Published in:Journal of computational physics 2020-11, Vol.421, p.109735, Article 109735
Main Authors: Peng, Zhuogang, McClarren, Ryan G., Frank, Martin
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Basis functions
Cartesian coordinates
Computational efficiency
Computational physics
Computing costs
Computing time
Low-rank approximation
Mathematical analysis
Operators (mathematics)
Radiation transport
Spherical harmonics
Tensors
Time dependence
Transport equations
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Summary:•A low-rank scheme of the radiation transport equation is developed.•The time evolution of the radiation intensity is constrained in low-rank manifolds.•Computational cost and memory are significantly reduced without sacrificing accuracy.•A major improvement in accuracy can be obtained by a slight increase in memory. The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational cost. In this work, a dynamical low-rank approximation method is developed for the time-dependent radiation transport equation in 1-D and 2-D Cartesian geometries. Using a finite volume discretization in space and a spherical harmonics basis in angle, we construct a system that evolves on a low-rank manifold via an operator splitting approach. Numerical results on five test problems demonstrate that the low-rank solution requires less memory and computational time than solving the full rank equations with the same accuracy. It is furthermore shown that the low-rank algorithm can obtain high-fidelity results by increasing the number of basis functions while keeping the rank fixed.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2020.109735