A data-based conservative reduced collision model for the Boltzmann equation
Abstract
The evaluation of the quadratic collision operator is one of the major computational bottlenecks in solving the Boltzmann equation owing to the high dimensionality and the nonlinear structure of the collision term. In this work, a conservative reduced collision (RC) model is developed within the discrete velocity framework. The bilinear collision operator is approximated through a kernel tensor preassembled with the problem-dependent reduced bases for the distribution function and the collision term. Consequently, online evaluation of the quadratic collision operator is reduced to tensor contractions. Exact discrete conservation of mass, momentum, and energy is enforced by constructing the collision basis in the orthogonal complement of the space spanned by the discrete collision invariants. Several numerical experiments validate the efficiency of this RC model.
Related
- Reduced order model for parametric Boltzmann equation and its application to inverse problems
- A Structure-Preserving Effective Linear Approximation of the Quantum Boltzmann Collision Operator
- Wigner-Eckart Factorization of the Polyatomic Boltzmann Collision Operator
- A fast Laguerre--Fourier spectral method for the polyatomic Boltzmann collision operator with continuous internal energy
- The Boltzmann-BGK model with nontrivial collision frequency near vacuum
BibTeX
@misc{zhang2026databased,
title = {{A data-based conservative reduced collision model for the Boltzmann equation}},
author = {Pei Zhang and Yanli Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25398},
eprint = {2610.25398},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25398},
}
RIS
TY - UNPB
TI - A data-based conservative reduced collision model for the Boltzmann equation
AU - Pei Zhang
AU - Yanli Wang
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.25398
UR - https://arxiv.org/abs/2610.25398
AB - The evaluation of the quadratic collision operator is one of the major computational bottlenecks in solving the Boltzmann equation owing to the high dimensionality and the nonlinear structure of the collision term. In this work, a conservative reduced collision (RC) model is developed within the discrete velocity framework. The bilinear collision operator is approximated through a kernel tensor preassembled with the problem-dependent reduced bases for the distribution function and the collision term. Consequently, online evaluation of the quadratic collision operator is reduced to tensor contractions. Exact discrete conservation of mass, momentum, and energy is enforced by constructing the collision basis in the orthogonal complement of the space spanned by the discrete collision invariants. Several numerical experiments validate the efficiency of this RC model.
ER -