Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes

Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-...

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Bibliographic Details
Published in:Journal of computational physics 2011-02, Vol.230 (3), p.763-788
Main Authors: Wang, Yaqi, Ragusa, Jean C.
Format: Article
Language:English
Subjects:
Adaptive mesh refinement
BOLTZMANN EQUATION
Boltzmann transport equation
Computational techniques
Discontinuous finite element techniques
DISCRETE ORDINATE METHOD
Discrete ordinates method
Error estimates
Errors
Estimates
Exact sciences and technology
Galerkin methods
Goal-oriented mesh refinement
ITERATIVE METHODS
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematical methods in physics
Mathematical models
MESH GENERATION
NUCLEAR PHYSICS AND RADIATION PHYSICS
Physics
RADIATION TRANSPORT
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Summary:Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2010.10.018