# Quadratic Finite Element Method for 1D Deterministic Transport

## Abstract

In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 15013672

- Report Number(s):
- UCRL-CONF-201715

TRN: US0801236

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Conference

- Resource Relation:
- Conference: Presented at: 2004 American Nuclear Society Annual Meeting, Pittsburgh, PA, United States, Jun 13 - Jun 17, 2004

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 22 GENERAL STUDIES OF NUCLEAR REACTORS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; APPROXIMATIONS; CONVERGENCE; DISCRETE ORDINATE METHOD; FINITE ELEMENT METHOD; GEOMETRY; NUMERICAL SOLUTION; RESOLUTION; TRANSPORT

### Citation Formats

```
Tolar, Jr., D R, and Ferguson, J M.
```*Quadratic Finite Element Method for 1D Deterministic Transport*. United States: N. p., 2004.
Web.

```
Tolar, Jr., D R, & Ferguson, J M.
```*Quadratic Finite Element Method for 1D Deterministic Transport*. United States.

```
Tolar, Jr., D R, and Ferguson, J M. Tue .
"Quadratic Finite Element Method for 1D Deterministic Transport". United States. https://www.osti.gov/servlets/purl/15013672.
```

```
@article{osti_15013672,
```

title = {Quadratic Finite Element Method for 1D Deterministic Transport},

author = {Tolar, Jr., D R and Ferguson, J M},

abstractNote = {In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Tue Jan 06 00:00:00 EST 2004},

month = {Tue Jan 06 00:00:00 EST 2004}

}

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