A Conservative Multi-Level Adaptive Velocity-Space Method for the Discrete Unified Gas-Kinetic Scheme
Abstract
Multiscale gas flows often span a wide range of Knudsen numbers, from near-continuum to highly rarefied and strongly nonequilibrium conditions. Such flows require kinetic solvers that remain accurate across these regimes. The discrete unified gas-kinetic scheme (DUGKS) provides a unified description, but its computational cost and memory consumption are dominated by the size of the discrete velocity space. To alleviate this bottleneck, this work develops the multi-level velocity-space adaptive discrete unified gas-kinetic scheme (MLVS-DUGKS), reducing velocity-space redundancy while preserving accuracy and conservation. The method identifies the velocity-space requirements of individual physical cells from their distribution functions and groups these requirements into a small number of shared representative velocity spaces. This organization retains sensitivity to different local flow states without constructing an independent velocity space for every physical cell. A linear moment-constrained correction is incorporated to maintain discrete compatibility and conservative data transfer between representative spaces. Benchmark simulations spanning near-continuum to highly rarefied regimes show close agreement with the uniform-velocity-space DUGKS (UVS-DUGKS). For the cylinder and two-cavity problems, the average number of discrete velocity points is reduced by approximately one order of magnitude, yielding speedups of $7.00−−7.93$ and GPU-memory reductions by factors of $6.73−−7.49$. As a result, the MLVS-DUGKS provides an efficient tool for the simulation of multiscale nonequilibrium gas flows.
Related
- A nonequilibrium-capturing unified gas-kinetic scheme I: discrete orthogonal basis construction and expansion on velocity space
- A Fully Discrete, Mass-Conservative Adaptive Discontinuous Spectral-Element Method for the One-Dimensional Richards Equation in Mixed Form
- Vectorial discrete unified gas kinetic scheme for continuum compressible flows
- Unified Dynamics of Black-Hole Interiors: From Geometric to Scalar-Kinetic Dominance
- Harmonic Balance Unified Gas-Kinetic Scheme for Multiscale Periodic Flows
BibTeX
@misc{ren2026conservative,
title = {{A Conservative Multi-Level Adaptive Velocity-Space Method for the Discrete Unified Gas-Kinetic Scheme}},
author = {Weijie Ren and Hang Yu and Zhengyu Tian and Wenjia Xie and XiaoQiang Fan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.35258},
eprint = {2609.35258},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35258},
}
RIS
TY - UNPB
TI - A Conservative Multi-Level Adaptive Velocity-Space Method for the Discrete Unified Gas-Kinetic Scheme
AU - Weijie Ren
AU - Hang Yu
AU - Zhengyu Tian
AU - Wenjia Xie
AU - XiaoQiang Fan
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2609.35258
UR - https://arxiv.org/abs/2609.35258
AB - Multiscale gas flows often span a wide range of Knudsen numbers, from near-continuum to highly rarefied and strongly nonequilibrium conditions. Such flows require kinetic solvers that remain accurate across these regimes. The discrete unified gas-kinetic scheme (DUGKS) provides a unified description, but its computational cost and memory consumption are dominated by the size of the discrete velocity space. To alleviate this bottleneck, this work develops the multi-level velocity-space adaptive discrete unified gas-kinetic scheme (MLVS-DUGKS), reducing velocity-space redundancy while preserving accuracy and conservation. The method identifies the velocity-space requirements of individual physical cells from their distribution functions and groups these requirements into a small number of shared representative velocity spaces. This organization retains sensitivity to different local flow states without constructing an independent velocity space for every physical cell. A linear moment-constrained correction is incorporated to maintain discrete compatibility and conservative data transfer between representative spaces. Benchmark simulations spanning near-continuum to highly rarefied regimes show close agreement with the uniform-velocity-space DUGKS (UVS-DUGKS). For the cylinder and two-cavity problems, the average number of discrete velocity points is reduced by approximately one order of magnitude, yielding speedups of $7.00−−7.93$ and GPU-memory reductions by factors of $6.73−−7.49$. As a result, the MLVS-DUGKS provides an efficient tool for the simulation of multiscale nonequilibrium gas flows.
ER -