可压缩Navier--Stokes--Fourier方程的梯度重构格子玻尔兹曼方法
A Gradient-Reconstruction Lattice Boltzmann Method for Compressible Navier--Stokes--Fourier Equations
- Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
提出一种梯度重构格子玻尔兹曼方法，在不牺牲紧凑模板和局部性的前提下求解可压缩Navier--Stokes--Fourier方程，仅输运守恒量，从分布非平衡部分恢复梯度，相比输运通量方案内存更少、吞吐量高4.9倍，并验证于激波解和超声速涡。
中文摘要 AI 辅助
达到可压缩流动通常迫使格子玻尔兹曼方法放弃使其高效的紧凑模板或严格局部性。我们两者都不放弃，通过一种仅输运守恒的质量、动量和能量的方案求解可压缩Navier--Stokes--Fourier方程。粘性应力和热通量依赖于速度和温度梯度。为了捕获它们，现有的可压缩方案超越了守恒场的单一格子。它们扩大速度集，将应力和热通量作为额外的输运场携带，将能量放在单独的网格上，或者放弃精确流式而采用离格平流。我们则从碰撞内已经存在的分布的非平衡部分恢复梯度。除守恒状态外没有输运任何场，不读取邻居，流式保持精确，并且每个计算都以单精度运行。该方法携带五个场，而输运通量方案携带十四个场，内存占用仅为后者的一小部分，吞吐量是其4.9倍。通过与精确的Sod和Becker激波解以及超声速Taylor--Green涡的验证，它在动能上跟踪直接数值模拟参考，并在两个耗散率上保持在参考求解器散布范围内。
英文摘要
Reaching compressible flow has usually forced lattice Boltzmann methods to abandon the compact stencil or the strict locality that make them efficient. We give up neither, solving the compressible Navier--Stokes--Fourier equations with a scheme that transports only the conserved mass, momentum and energy. The viscous stress and heat flux depend on gradients of the velocity and temperature. To capture them, existing compressible schemes go beyond a single lattice of the conserved fields. They enlarge the velocity set, carry the stress and heat flux as extra transported fields, place the energy on a separate grid, or give up exact streaming for an off-lattice advection. We instead recover the gradients from the non-equilibrium part of the distributions already present, inside the collision. No field beyond the conserved state is transported, no neighbour is read, streaming stays exact, and every computation runs in single precision. The method carries five fields where a transported-flux scheme carries fourteen, at a fraction of the memory and $4.9$ times the throughput. Verified against the exact Sod and Becker shock solutions and a supersonic Taylor--Green vortex, it tracks the direct-numerical-simulation reference on the kinetic energy and stays within the reference-solver spread on both dissipation rates.
