[论文解读] Local kinetic sensors for adaptive mesh and algorithm refinement

R. M. Strässle, S. A. Hosseini+1 more|arXiv (Cornell University)|Mar 13, 2026

Lattice Boltzmann Simulation Studies被引用 0

一句话总结

本文介绍用于自适应网格和算法细化（AMAR）的局部动力学细化传感器，利用分布函数信息实现可扩展的局部标准，在一个离散速度Boltzmann求解器上得到验证。

ABSTRACT

This paper presents novel refinement sensors for the application to adaptive mesh and algorithm refinement (AMAR) with kinetic models, such as discrete velocity and lattice Boltzmann methods. While refinement criteria for AMAR based on macroscopic variables can be replicated in a purely local, and therefore more scalable, way, the main advantage that can be leveraged when working with discrete velocity and lattice Boltzmann methods is the accessibility of information from the one-particle distribution function. With this accessibility, a novel palette of refinement sensors is introduced, allowing for a set of neatly tailored refinement criteria applicable to resolve characteristic flows features in many relevant domains of fluid mechanics, for instance, those emerging in compressible, turbulent, and non-equilibrium flows or non-ideal fluids. After detailed validation, novel refinement sensors are showcased for the application of adaptive mesh refinement (AMR) to a discrete velocity Boltzmann solver for compressible, viscous, and non-equilibrium flows, demonstrating promising results. The proposed sensors establish an accurate, efficient and scalable approach to kinetic simulations with AMAR, offering a valuable tool for studying complex problems in fluid dynamics and paving the way for future extensions to more specific flow problems.

研究动机与目标

• 为动理模型定制的细化传感器的需要提供动机，而不仅仅是宏观指标。
• 开发一套利用单粒子分布函数信息的局部传感器。
• 确保传感器在并行高性能计算中是局部、高效且可扩展的。
• 在对compressible、粘性和非平衡流的守恒时空自适应网格细化框架中演示传感器的应用。
• 讨论对特定流场场景和非理想流体的潜在扩展。

提出的方法

• 描述具有双分布（f 和 g）和准平衡形式的一致动力学模型以捕获可变的普朗特数。
• 构建基于Hermite/Ghermite的平衡态和准平衡态，覆盖对 f 的 N=3/4 阶、对 g 的 N=2 阶的适当阶次。
• 实现一个完全守恒、时间显式的有限体积离散化，带有BGK型碰撞算子分裂为两个弛豫时间（τ1，τ2）。
• 使用双分布框架表示平移和非平移能量，使能够从动力学场在局部计算类宏观诊断量。
• 采用静态块结构化AMR，带有通量守恒回流（refluxing）和时间子循环，以在各等级保持统一的 CFL。

Figure 1: Exemplary two-level grid layout with $r_{l}=2$ for the illustration of level-wise boundary conditions (BCs) and conservative refluxing. The cell coordinates of the coarser level are denoted with ( $i$ , $j$ ) and the finer level with ( $v$ , $w$ ), respectively Strässle et al. [ 2025 ] .

实验结果

研究问题

• RQ1 可以定义哪些局部动力学指标来触发动理模型的AMAR自适应细化？
• RQ2 如何利用单粒子分布信息来实现可扩展的细化，而不仅依赖宏观梯度？
• RQ3 在AMR网格上，提出的传感器能否准确捕捉可压缩、粘性、非平衡和非理想流动的特征？
• RQ4 在并行环境中，动力学细化传感器与宏观标准相比在准确性、效率和可扩展性方面的表现如何？

主要发现

• 引入适用于动理模型的AMAR局部动力学细化传感器套件。
• 证明基于分布函数信息的传感器在某些流动情形下可优于仅基于宏观梯度的标准。
• 在用于可压缩、粘性和非平衡流的离散速度Boltzmann求解器的自适应网格细化上验证传感器。
• 显示动力学传感器使AMR在复杂流体动力学问题上具有高精度、高效率和可扩展性。

Figure 2: Illustration of the updates and level-wise information exchanges in the subcycling approach. BC refers to the boundary conditions of type physical, synchronization and prolongation, whereas R refers to restriction and CR to the refluxing correction pass. The horizontal axis marks time and