A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

doi:10.13182/NSE16-36

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

Journal Article · Thu Feb 08 00:00:00 EST 2018 · Nuclear Science and Engineering

DOI:https://doi.org/10.13182/NSE16-36· OSTI ID:1338753

Bolding, Simon R. ^[1]; Cleveland, Mathew Allen ^[2]; Morel, Jim E. ^[1]

Texas A & M Univ., College Station, TX (United States). Dept. of Nuclear Engineering
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S₂ equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.

Research Organization:: Los Alamos National Laboratory (LANL); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Nuclear Energy (NE). Nuclear Energy University Programs (NEUP)

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396; NA0002376

OSTI ID:: 1338753

Alternate ID(s):: OSTI ID: 1673359

Report Number(s):: LA-UR--14-29653; LA-UR-16-20497

Journal Information:: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 185; ISSN 0029-5639

Publisher:: American Nuclear Society - Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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