# A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes

## Abstract

We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h{sup 2}) convergence of the scalar flux on orthogonal, random, and multi-level meshes.

- Authors:

- Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37831 (United States)
- Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 (United States)
- Department of Nuclear Engineering, Texas A and M University, College Station, TX 77843 (United States)

- Publication Date:

- OSTI Identifier:
- 22382107

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 273; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; APPROXIMATIONS; CONVERGENCE; DIFFUSION EQUATIONS; MATHEMATICAL SOLUTIONS; NEUTRAL-PARTICLE TRANSPORT; NONLINEAR PROBLEMS; RADIATION PROTECTION; RANDOMNESS; SCALARS; SCATTERING; TRANSPORT THEORY

### Citation Formats

```
Wieselquist, William A., E-mail: wieselquiswa@ornl.gov, Anistratov, Dmitriy Y., and Morel, Jim E.
```*A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes*. United States: N. p., 2014.
Web. doi:10.1016/J.JCP.2014.05.011.

```
Wieselquist, William A., E-mail: wieselquiswa@ornl.gov, Anistratov, Dmitriy Y., & Morel, Jim E.
```*A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes*. United States. doi:10.1016/J.JCP.2014.05.011.

```
Wieselquist, William A., E-mail: wieselquiswa@ornl.gov, Anistratov, Dmitriy Y., and Morel, Jim E. Mon .
"A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes". United States. doi:10.1016/J.JCP.2014.05.011.
```

```
@article{osti_22382107,
```

title = {A cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes},

author = {Wieselquist, William A., E-mail: wieselquiswa@ornl.gov and Anistratov, Dmitriy Y. and Morel, Jim E.},

abstractNote = {We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h{sup 2}) convergence of the scalar flux on orthogonal, random, and multi-level meshes.},

doi = {10.1016/J.JCP.2014.05.011},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = ,

volume = 273,

place = {United States},

year = {2014},

month = {9}

}