A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Abstract

A new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup $P_1,$ $P_{1/3},$ and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

Keywords:

• Boltzmann transport equation
• variable Eddington tensor
• radiation diffusion
• model order reduction
• nonlinear PDEs

Acknowledgment

The content of the information does not necessarily reflect the position or the policy of the federal government, and no official endorsement should be inferred.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research project was funded by the Sandia National Laboratory, Light Speed Grand Challenge, LDRD, Strong Shock Thrust. This work was supported by the U.S. Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001).