Generalized Reference Fields and Source Interpolation for the Difference Formulation of Radiation Transport
In the difference formulation for the transport of thermally emitted photons, the photon intensity is defined relative to a reference field, the black body at the local material temperature. This choice of reference field combines the separate emission and absorption terms that nearly cancel, removing the dominant cause of noise in the Monte Carlo solution of thick systems, but introduces time and space derivative source terms that can not be determined until the end of the time step. The space derivative source term can also lead to noise induced crashes under certain conditions where the real physical photon intensity differs strongly from a black body at the local material temperature. In this paper, we consider a difference formulation relative to the material temperature at the beginning of the time step, or in cases where an alternative temperature better describes the radiation field, that temperature. The result is a method where iterative solution of the material energy equation is efficient and noise induced crashes are avoided. We couple our generalized reference field scheme with an ad hoc interpolation of the space derivative source, resulting in an algorithm that produces the correct flux between zones as the physical system approaches the thick limit.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 972417
- Report Number(s):
- LLNL-JRNL-411084; JCTPAH; TRN: US1001597
- Journal Information:
- Journal of Computational Physics, Vol. 229, Issue 5; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Generalized Subtraction Schemes for the Difference Formulation in Radiation Transport
Accurate and efficient radiation transport in optically thick media -- by means of the Symbolic Implicit Monte Carlo method in the difference formulation