# EDW S{sub n} differencing compared to Monte Carlo for zero-c problems

## Abstract

Both the discrete ordinates (S{sub n}) method and the Monte Carlo method can be used to solve large three-dimensional steady-state transport problems. Because Monte Carlo is simpler (in principle) and offers the advantages of precise geometric description with robust particle physics treatments, it is often selected as the method of choice. In spite of the positive aspects of Monte Carlo, key disadvantages are processing time, the unavoidable element of uncertainty in the computations, and the lack of a global (phase-space) solution. Discrete ordinates methods require that the problem geometry be approximated using a spatial grid and require a suitable cross-section library, not to mention the need for large amounts of computer memory and storage. However, provided the resources are available, S{sub n} methods are advantageous in that they are quite fast (compared to Monte Carlo). Furthermore, S{sub n} methods provide a global flux solution, with accuracy defined by the cross-section data and the spatial mesh interval, which can be easily controlled. Because of the inherent independence of each particle history, Monte Carlo calculations can be easily implemented on parallel computers. Parallelization of the deterministic Boltzmann equation, coupled in angle, energy, and spatial domains, is not straightforward. However, the authors havemore »

- Authors:

- Air Force Academy, CO (United States)
- Pennsylvania State Univ., University Park, PA (United States)

- Publication Date:

- OSTI Identifier:
- 678139

- Report Number(s):
- CONF-990605-

Journal ID: TANSAO; ISSN 0003-018X; TRN: 99:009124

- Resource Type:
- Journal Article

- Journal Name:
- Transactions of the American Nuclear Society

- Additional Journal Information:
- Journal Volume: 80; Conference: 1999 annual meeting of the American Nuclear Society (ANS), Boston, MA (United States), 6-10 Jun 1999; Other Information: PBD: 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; DISCRETE ORDINATE METHOD; MONTE CARLO METHOD; TRANSPORT THEORY; THREE-DIMENSIONAL CALCULATIONS; P CODES; MESH GENERATION; WEIGHTING FUNCTIONS

### Citation Formats

```
Sjoden, G.E., Haghighat, A., and Patchimpattapong, A.
```*EDW S{sub n} differencing compared to Monte Carlo for zero-c problems*. United States: N. p., 1999.
Web.

```
Sjoden, G.E., Haghighat, A., & Patchimpattapong, A.
```*EDW S{sub n} differencing compared to Monte Carlo for zero-c problems*. United States.

```
Sjoden, G.E., Haghighat, A., and Patchimpattapong, A. Wed .
"EDW S{sub n} differencing compared to Monte Carlo for zero-c problems". United States.
```

```
@article{osti_678139,
```

title = {EDW S{sub n} differencing compared to Monte Carlo for zero-c problems},

author = {Sjoden, G.E. and Haghighat, A. and Patchimpattapong, A.},

abstractNote = {Both the discrete ordinates (S{sub n}) method and the Monte Carlo method can be used to solve large three-dimensional steady-state transport problems. Because Monte Carlo is simpler (in principle) and offers the advantages of precise geometric description with robust particle physics treatments, it is often selected as the method of choice. In spite of the positive aspects of Monte Carlo, key disadvantages are processing time, the unavoidable element of uncertainty in the computations, and the lack of a global (phase-space) solution. Discrete ordinates methods require that the problem geometry be approximated using a spatial grid and require a suitable cross-section library, not to mention the need for large amounts of computer memory and storage. However, provided the resources are available, S{sub n} methods are advantageous in that they are quite fast (compared to Monte Carlo). Furthermore, S{sub n} methods provide a global flux solution, with accuracy defined by the cross-section data and the spatial mesh interval, which can be easily controlled. Because of the inherent independence of each particle history, Monte Carlo calculations can be easily implemented on parallel computers. Parallelization of the deterministic Boltzmann equation, coupled in angle, energy, and spatial domains, is not straightforward. However, the authors have developed the PENTRAN three-dimensional S{sub n} code that with automatic memory partitioning and hybrid domain decomposition (space, energy, and/or angle) is capable of solving large problems in a short time. Historically, a key area of difficulty for S{sub n} methods is in solving transport problems with materials that have little or no particle scattering. In such cases, particle flux solutions are prone to ray effects, wherein source particles stream uncollided through the geometry along a single discrete direction. Rather than smooth, physical solutions, ray effects yield unphysical oscillations. The purpose herein is to demonstrate that in the case of very low or no scattering, ray effects in an S{sub n} calculation can be virtually eliminated by using a coarse spatial mesh with an accurate, exponential-based differencing scheme. Further, the authors demonstrate that in considering the computational cost and the amount of information provided, the S{sub n} method with the exponential directional weighted (EDW) scheme is a superior technique for this problem.},

doi = {},

journal = {Transactions of the American Nuclear Society},

number = ,

volume = 80,

place = {United States},

year = {1999},

month = {9}

}