AI 中文总结
该研究提出一种由符号编译器自动推导的三维可压缩Navier-Stokes-Fourier方程格子玻尔兹曼格式，经精确解与基准数据验证，在超音速Taylor-Green涡模拟中表现优于7种对比求解器。
AI 中文摘要
本文提出一种三维可压缩Navier-Stokes-Fourier方程的格子玻尔兹曼格式，该格式由符号编译器根据所声明的系统自动推导得出，已通过精确解和已发表的参考数据验证。所声明的系统将粘性应力和热通量作为输运状态，以单精度在D3Q7格子上离散化。针对精确的Sod和Becker解，捕捉到的激波厚度呈一阶收敛。在马赫数M₀=1.25的超音速Taylor-Green涡中，512³规模的该格式与参考胀量耗散的匹配度优于其他7种对比求解器，比次优求解器高出30%。该求解器中的每个算子，包括生成的碰撞项、本构封闭项以及添加的激波传感器，仅读取其作用的单元格，数据仅通过沿格子特征的流场传递至相邻单元格。
英文摘要
A lattice Boltzmann scheme for the three-dimensional compressible Navier--Stokes--Fourier equations, derived automatically from the declared system by a symbolic compiler, is validated against exact solutions and published reference data. The declared system carries the viscous stress and the heat flux as transported state, and is discretized on a D3Q7 lattice in single precision. Against the exact Sod and Becker solutions the captured shock thickness converges at first order. On the supersonic Taylor-Green vortex at $M_0 = 1.25$ the scheme at $512^3$ matches the reference dilatational dissipation more closely than seven compared solvers, by thirty percent over the next best. Every operator in this solver, the generated collision and constitutive closure and the added shock sensor alike, reads only the cell it acts on, and data reaches a neighbor only by streaming along the lattice characteristics.
