DDPS | Reduced order models for thermal radiative transfer problems based on moment equations & POD

In this DDPS talk from Aug. 13, 2021, Dmitriy Anistratov, a professor of nuclear engineering at North Carolina State University, presents a new group of reduced-order models (ROMs) for nonlinear thermal radiative transfer (TRT) problems.

ROMs are formulated by means of the nonlinear projective approach and data compression techniques. The nonlinear projection is applied to the Boltzmann transport equation to derive a hierarchy of low-order moment equations. The Eddington (quasi-diffusion) tensor that provides exact closure for the system of moment equations is approximated via one of data-based methods of model-order reduction. These methods are the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). Its low-rank approximation is performed over the whole phase space and time interval based on available data. The ROMs preserve fundamental physical properties and asymptotic of the TRT solution. Numerical results show that these models are accurate for simulations of evolving radiation and heat waves even with very low-rank representations of the Eddington tensor. As the rank of the approximation is increased, the errors of ROM solutions gradually decreases. The proposed approach for developing ROMs can be applied to a wide class of multi-physics high-energy density problems, e.g. radiative hydrodynamics. This is joint work with Joseph Coale, North Carolina State University.

Short bio:
Dmitriy Anistratov is a Professor of Nuclear Engineering at NC State University. He works in the field of computational physics, numerical analysis, and particle transport theory. His research involves development of iteration methods for the Boltzmann transport equation, computational methods for multi-physics and multiscale problems, mathematical models of particle transport in various physical systems, reduced-order models. Prior to joining NC State, he was a research staff member at Keldysh Institute for Applied Mathematics and Institute for Mathematical Modeling of Russian Academy of Sciences, Visiting Assistant Professor at the Department of Nuclear Engineering at Texas A&M University. D. Anistratov has served as a guest scientist to the computational transport group (CCS-2) at Los Alamos National Laboratory. He is currently a guest scientist at the Center of Applied Scientific Computing at Lawrence Livermore National Laboratory. D. Anistratov received his Ph. D. in Mathematical and Physical Sciences from Russian Academy of Sciences and MS in Physics from Moscow Institute of Physics and Technology.

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