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, within which the flow varies from near-continuum to highly rarefied and strongly nonequilibrium states. Such flows require kinetic solvers that remain accurate across the entire range. The discrete unified gas-kinetic scheme (DUGKS) provides such 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 improves the DUGKS with multi-level adaptive velocity-space discretization (MLVS-DUGKS), reducing velocity-space redundancy while preserving accuracy and conservation. This method identify the velocity-space requirements of each physical cell from its distribution function, and then groups these requirements into a small number of 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 velocity spaces. Benchmark simulations spanning near-continuum to highly rarefied regimes show close agreement with the uniform-velocity-space DUGKS (UVS-DUGKS). For the computationally demanding cases, the average number of discrete velocity points is reduced by approximately one order of magnitude, yielding speedups of 6.67--7.51 and GPU-memory reductions by factors of 6.15--6.88. A threshold study further shows that the actual computational performance is governed by a balance between velocity-space compression and cross-level coupling overhead. The MLVS-DUGKS thus provides an accurate, conservative, and computationally efficient framework for multiscale nonequilibrium-flow simulations.