# A Residual Monte Carlo Method for Spatially Discrete, Angularly Continuous Radiation Transport

## Abstract

Residual Monte Carlo provides exponential convergence of statistical error with respect to the number of particle histories. In the past, residual Monte Carlo has been applied to a variety of angularly discrete radiation-transport problems. Here, we apply residual Monte Carlo to spatially discrete, angularly continuous transport. By maintaining angular continuity, our method avoids the deficiencies of angular discretizations, such as ray effects. For planar geometry and step differencing, we use the corresponding integral transport equation to calculate an angularly independent residual from the scalar flux in each stage of residual Monte Carlo. We then demonstrate that the resulting residual Monte Carlo method does indeed converge exponentially to within machine precision of the exact step differenced solution.

- Authors:

- Los Alamos National Laboratory

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- DOE/LANL

- OSTI Identifier:
- 1044108

- Report Number(s):
- LA-UR-12-22311

TRN: US1203331

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Conference

- Resource Relation:
- Conference: American Nuclear Society Annual Meeting ; 2012-06-24 - 2012-06-24 ; Chicago, Illinois, United States

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; CONVERGENCE; GEOMETRY; MONTE CARLO METHOD; RADIATION TRANSPORT; SCALARS; TRANSPORT

### Citation Formats

```
Wollaeger, Ryan T., and Densmore, Jeffery D.
```*A Residual Monte Carlo Method for Spatially Discrete, Angularly Continuous Radiation Transport*. United States: N. p., 2012.
Web.

```
Wollaeger, Ryan T., & Densmore, Jeffery D.
```*A Residual Monte Carlo Method for Spatially Discrete, Angularly Continuous Radiation Transport*. United States.

```
Wollaeger, Ryan T., and Densmore, Jeffery D. Tue .
"A Residual Monte Carlo Method for Spatially Discrete, Angularly Continuous Radiation Transport". United States. https://www.osti.gov/servlets/purl/1044108.
```

```
@article{osti_1044108,
```

title = {A Residual Monte Carlo Method for Spatially Discrete, Angularly Continuous Radiation Transport},

author = {Wollaeger, Ryan T. and Densmore, Jeffery D.},

abstractNote = {Residual Monte Carlo provides exponential convergence of statistical error with respect to the number of particle histories. In the past, residual Monte Carlo has been applied to a variety of angularly discrete radiation-transport problems. Here, we apply residual Monte Carlo to spatially discrete, angularly continuous transport. By maintaining angular continuity, our method avoids the deficiencies of angular discretizations, such as ray effects. For planar geometry and step differencing, we use the corresponding integral transport equation to calculate an angularly independent residual from the scalar flux in each stage of residual Monte Carlo. We then demonstrate that the resulting residual Monte Carlo method does indeed converge exponentially to within machine precision of the exact step differenced solution.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {6}

}