A low-rank method for two-dimensional time-dependent radiation transport calculations

Abstract

The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational cost. In this work, a dynamical low-rank approximation method is developed for the time-dependent radiation transport equation in 1-D and 2-D Cartesian geometries. Using a finite volume discretization in space and a spherical harmonics basis in angle, we construct a system that evolves on a low-rank manifold via an operator splitting approach. Numerical results on five test problems demonstrate that the low-rank solution requires less memory than solving the full rank equations with the same accuracy. It is furthermore shown that the low-rank algorithm can obtain high-fidelity results at a moderate extra cost by increasing the number of basis functions while keeping the rank fixed.

arXiv admin note: text overlap with arXiv:1906.09940

References in corpus (7)

• A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
• A semi-Lagrangian Vlasov solver in tensor train format
• An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
• A low-rank projector-splitting integrator for the Vlasov--Maxwell equations with divergence correction
• Implicit Filtered PN for High-Energy Density Thermal Radiation Transport using Discontinuous Galerkin Finite Elements
• Angular adaptivity with spherical harmonics for Boltzmann transport
• A low-rank method for time-dependent transport calculations

Cited by in corpus (12)

• An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
• A mass, momentum, and energy conservative dynamical low-rank scheme for the Vlasov equation
• A high-order / low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations
• A robust and conservative dynamical low-rank algorithm
• A low-rank power iteration scheme for neutron transport criticality problems
• A sweep-based low-rank method for the discrete ordinate transport equation
• Efficient 6D Vlasov simulation using the dynamical low-rank framework Ensign
• A Reduced-Order Model for Nonlinear Radiative Transfer Problems Based on Moment Equations and POD-Petrov-Galerkin Projection of the Normalized Boltzmann Transport Equation
• A reduced basis method for radiative transfer equation
• Reduced-Order Models for Thermal Radiative Transfer Based on POD-Galerkin Method and Low-Order Quasidiffusion Equations
• A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure based on Data-Driven Shape Function
• Reduced order models for nonlinear radiative transfer based on moment equations and POD/DMD of Eddington tensor