# A hybrid approach to the neutron transport K-eigenvalue problem using NDA-based algorithms

## Abstract

In order to provide more physically accurate solutions to the neutron transport equation it has become increasingly popular to use Monte Carlo simulation to model nuclear reactor dynamics. These Monte Carlo methods can be extremely expensive, so we turn to a class of methods known as hybrid methods, which combine known deterministic and stochastic techniques to solve the transport equation. In our work, we show that we can simulate the action of a transport sweep using a Monte Carlo simulation in order to solve the k-eigenvalue problem. We'll accelerate the solution using nonlinear diffusion acceleration (NDA) as in [1,2]. Our work extends the results in [1] to use Monte Carlo simulation as the high-order solver. (authors)

- Authors:

- North Carolina State University, Raleigh, NC 27606 (United States)
- Theory Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

- Publication Date:

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

- OSTI Identifier:
- 22212848

- 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; 12 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; ACCELERATION; COMPUTERIZED SIMULATION; EIGENFUNCTIONS; EIGENVALUES; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; NEUTRON FLUX; NEUTRON TRANSPORT; NEUTRON TRANSPORT THEORY; NONLINEAR PROBLEMS; REACTORS; STOCHASTIC PROCESSES

### Citation Formats

```
Willert, J. A., Kelley, C. T., Knoll, D. A., and Park, H.
```*A hybrid approach to the neutron transport K-eigenvalue problem using NDA-based algorithms*. United States: N. p., 2013.
Web.

```
Willert, J. A., Kelley, C. T., Knoll, D. A., & Park, H.
```*A hybrid approach to the neutron transport K-eigenvalue problem using NDA-based algorithms*. United States.

```
Willert, J. A., Kelley, C. T., Knoll, D. A., and Park, H. Mon .
"A hybrid approach to the neutron transport K-eigenvalue problem using NDA-based algorithms". United States.
```

```
@article{osti_22212848,
```

title = {A hybrid approach to the neutron transport K-eigenvalue problem using NDA-based algorithms},

author = {Willert, J. A. and Kelley, C. T. and Knoll, D. A. and Park, H.},

abstractNote = {In order to provide more physically accurate solutions to the neutron transport equation it has become increasingly popular to use Monte Carlo simulation to model nuclear reactor dynamics. These Monte Carlo methods can be extremely expensive, so we turn to a class of methods known as hybrid methods, which combine known deterministic and stochastic techniques to solve the transport equation. In our work, we show that we can simulate the action of a transport sweep using a Monte Carlo simulation in order to solve the k-eigenvalue problem. We'll accelerate the solution using nonlinear diffusion acceleration (NDA) as in [1,2]. Our work extends the results in [1] to use Monte Carlo simulation as the high-order solver. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2013},

month = {7}

}

Other availability

Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.