# Monte Carlo solution of a semi-discrete transport equation

## Abstract

The authors present the S{sub {infinity}} method, a hybrid neutron transport method in which Monte Carlo particles traverse discrete space. The goal of any deterministic/stochastic hybrid method is to couple selected characters from each of the methods in hopes of producing a better method. The S{sub {infinity}} method has the features of the lumped, linear-discontinuous (LLD) spatial discretization, yet it has no ray-effects because of the continuous angular variable. They derive the S{sub {infinity}} method for the solid-state, mono-energetic transport equation in one-dimensional slab geometry with isotropic scattering and an isotropic internal source. They demonstrate the viability of the S{sub {infinity}} method by comparing their results favorably to analytic and deterministic results.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (US)

- Sponsoring Org.:
- USDOE Office of Defense Programs (DP) (US)

- OSTI Identifier:
- 756987

- Report Number(s):
- LA-UR-99-1131

TRN: US0003754

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: ANS, Math and Computations, Madrid (ES), No date supplied; Other Information: Conference held during 09/1999; PBD: 1 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; MONTE CARLO METHOD; NEUTRON TRANSPORT THEORY; STOCHASTIC PROCESSES; HYBRID SYSTEMS

### Citation Formats

```
Urbatsch, T.J., Morel, J.E., and Gulick, J.C.
```*Monte Carlo solution of a semi-discrete transport equation*. United States: N. p., 1999.
Web.

```
Urbatsch, T.J., Morel, J.E., & Gulick, J.C.
```*Monte Carlo solution of a semi-discrete transport equation*. United States.

```
Urbatsch, T.J., Morel, J.E., and Gulick, J.C. Wed .
"Monte Carlo solution of a semi-discrete transport equation". United States. https://www.osti.gov/servlets/purl/756987.
```

```
@article{osti_756987,
```

title = {Monte Carlo solution of a semi-discrete transport equation},

author = {Urbatsch, T.J. and Morel, J.E. and Gulick, J.C.},

abstractNote = {The authors present the S{sub {infinity}} method, a hybrid neutron transport method in which Monte Carlo particles traverse discrete space. The goal of any deterministic/stochastic hybrid method is to couple selected characters from each of the methods in hopes of producing a better method. The S{sub {infinity}} method has the features of the lumped, linear-discontinuous (LLD) spatial discretization, yet it has no ray-effects because of the continuous angular variable. They derive the S{sub {infinity}} method for the solid-state, mono-energetic transport equation in one-dimensional slab geometry with isotropic scattering and an isotropic internal source. They demonstrate the viability of the S{sub {infinity}} method by comparing their results favorably to analytic and deterministic results.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}