# A variable-order time-dependent neutron transport method for nuclear reactor kinetics using analytically-integrated space-time characteristics

## Abstract

A new time-dependent neutron transport method based on the method of characteristics (MOC) has been developed. Whereas most spatial kinetics methods treat time dependence through temporal discretization, this new method treats time dependence by defining the characteristics to span space and time. In this implementation regions are defined in space-time where the thickness of the region in time fulfills an analogous role to the time step in discretized methods. The time dependence of the local source is approximated using a truncated Taylor series expansion with high order derivatives approximated using backward differences, permitting the solution of the resulting space-time characteristic equation. To avoid a drastic increase in computational expense and memory requirements due to solving many discrete characteristics in the space-time planes, the temporal variation of the boundary source is similarly approximated. This allows the characteristics in the space-time plane to be represented analytically rather than discretely, resulting in an algorithm comparable in implementation and expense to one that arises from conventional time integration techniques. Furthermore, by defining the boundary flux time derivative in terms of the preceding local source time derivative and boundary flux time derivative, the need to store angularly-dependent data is avoided without approximating the angular dependencemore »

- Authors:

- Department of Nuclear Engineering and Radiological Sciences, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, MI, 48109-2104 (United States)

- Publication Date:

- Research Org.:
- American Nuclear Society, 555 North Kensington Avenue, La Grange Park, IL 60526 (United States)

- OSTI Identifier:
- 22212844

- Resource Type:
- Conference

- Resource Relation:
- Conference: M and C 2013: 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Sun Valley, ID (United States), 5-9 May 2013; Other Information: Country of input: France; 17 refs.; Related Information: In: Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013| 3016 p.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ALGORITHMS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; EQUATIONS; MATHEMATICAL SOLUTIONS; NEUTRON FLUX; NEUTRON TRANSPORT; REACTOR KINETICS; SERIES EXPANSION; SPACE-TIME; TIME DEPENDENCE; TRANSIENTS

### Citation Formats

```
Hoffman, A. J., and Lee, J. C.
```*A variable-order time-dependent neutron transport method for nuclear reactor kinetics using analytically-integrated space-time characteristics*. United States: N. p., 2013.
Web.

```
Hoffman, A. J., & Lee, J. C.
```*A variable-order time-dependent neutron transport method for nuclear reactor kinetics using analytically-integrated space-time characteristics*. United States.

```
Hoffman, A. J., and Lee, J. C. Mon .
"A variable-order time-dependent neutron transport method for nuclear reactor kinetics using analytically-integrated space-time characteristics". United States.
```

```
@article{osti_22212844,
```

title = {A variable-order time-dependent neutron transport method for nuclear reactor kinetics using analytically-integrated space-time characteristics},

author = {Hoffman, A. J. and Lee, J. C.},

abstractNote = {A new time-dependent neutron transport method based on the method of characteristics (MOC) has been developed. Whereas most spatial kinetics methods treat time dependence through temporal discretization, this new method treats time dependence by defining the characteristics to span space and time. In this implementation regions are defined in space-time where the thickness of the region in time fulfills an analogous role to the time step in discretized methods. The time dependence of the local source is approximated using a truncated Taylor series expansion with high order derivatives approximated using backward differences, permitting the solution of the resulting space-time characteristic equation. To avoid a drastic increase in computational expense and memory requirements due to solving many discrete characteristics in the space-time planes, the temporal variation of the boundary source is similarly approximated. This allows the characteristics in the space-time plane to be represented analytically rather than discretely, resulting in an algorithm comparable in implementation and expense to one that arises from conventional time integration techniques. Furthermore, by defining the boundary flux time derivative in terms of the preceding local source time derivative and boundary flux time derivative, the need to store angularly-dependent data is avoided without approximating the angular dependence of the angular flux time derivative. The accuracy of this method is assessed through implementation in the neutron transport code DeCART. The method is employed with variable-order local source representation to model a TWIGL transient. The results demonstrate that this method is accurate and more efficient than the discretized method. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2013},

month = {7}

}