# A Heterogeneous Medium Analytical Benchmark

## Abstract

A benchmark, called benchmark BLUE, has been developed for one-group neutral particle (neutron or photon) transport in a one-dimensional sub-critical heterogeneous plane parallel medium with surface illumination. General anisotropic scattering is accommodated through the Green's Function Method (GFM). Numerical Fourier transform inversion is used to generate the required Green's functions which are kernels to coupled integral equations that give the exiting angular fluxes. The interior scalar flux is then obtained through quadrature. A compound iterative procedure for quadrature order and slab surface source convergence provides highly accurate benchmark qualities (4- to 5- places of accuracy) results.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 757320

- Report Number(s):
- LA-UR-99-1280

TRN: US0004411

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

- Resource Type:
- Conference

- Resource Relation:
- Conference: M and C '99, Madrid (ES), 09/27/1999--09/30/1999; Other Information: PBD: 27 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; ACCURACY; BENCHMARKS; NEUTRON TRANSPORT; PHOTON TRANSPORT; GREEN FUNCTION; FOURIER TRANSFORMATION; ITERATIVE METHODS; INTEGRAL EQUATIONS; QUADRATURES; SCATTERING

### Citation Formats

```
Ganapol, B.D.
```*A Heterogeneous Medium Analytical Benchmark*. United States: N. p., 1999.
Web.

```
Ganapol, B.D.
```*A Heterogeneous Medium Analytical Benchmark*. United States.

```
Ganapol, B.D. Mon .
"A Heterogeneous Medium Analytical Benchmark". United States. https://www.osti.gov/servlets/purl/757320.
```

```
@article{osti_757320,
```

title = {A Heterogeneous Medium Analytical Benchmark},

author = {Ganapol, B.D.},

abstractNote = {A benchmark, called benchmark BLUE, has been developed for one-group neutral particle (neutron or photon) transport in a one-dimensional sub-critical heterogeneous plane parallel medium with surface illumination. General anisotropic scattering is accommodated through the Green's Function Method (GFM). Numerical Fourier transform inversion is used to generate the required Green's functions which are kernels to coupled integral equations that give the exiting angular fluxes. The interior scalar flux is then obtained through quadrature. A compound iterative procedure for quadrature order and slab surface source convergence provides highly accurate benchmark qualities (4- to 5- places of accuracy) results.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1999},

month = {9}

}

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