AI 中文总结
该研究开发了基于玻尔兹曼-BGK方程的动力学线性稳定性理论（kLST）及高性能计算框架，用于分析高马赫数激波的稳定性，揭示了动力学效应会使谱向更不稳定区域偏移，且实现了最高马赫数的激波kLST计算。
AI 中文摘要
高速可压缩流动中的激波包含有限厚度、高梯度区域，连续介质假设在此处存疑，且会出现平动非平衡现象，包括非麦克斯韦型微速度分布。经典激波稳定性分析依赖纳维-斯托克斯方程或矩封闭，无法保留激波内部的双峰速度分布。我们首次开发并应用了针对一维正激波的动力学线性稳定性理论（kLST），通过将玻尔兹曼-BGK方程关于动力学BE-BGK基流线性化来实现。扰动被定义在约化分布函数上，宏观场通过速度空间矩恢复，因此稳定性算子作用于速度分布函数（VDF）而非封闭的连续介质系统。该框架在近连续介质区通过可压缩库埃特本征值基准验证后，被应用于马赫数M_∞=1.2、3.0和4.0的氩气激波。低马赫数下，BE-BGK与吉尔巴格-保卢奇剖面几乎重合，谱呈现稳定连续分支；高马赫数下，对比麦克斯韦型与非平衡VDF基本征谱发现，动力学效应使谱向更不稳定区域偏移，因此即使宏观剖面已得到良好解析，连续介质预测仍可能遗漏重要变化。针对大型高马赫矩阵（O(10^5)个未知量及数十亿个非零元），我们开发了基于SLEPc/PETSc的并行基础设施：中等规模系统采用带MUMPS LU的移位反阿诺尔迪方法，最大规模系统采用带块雅可比ILU的雅可比-戴维森（JD）方法。空间/微速度耦合稀疏性导致严重的LU填充，使直接求解器受内存限制，从而推动JD方法的应用。我们计算了M_∞=4.0激波的kLST谱，其未知量达281088个，据我们所知，这是已报道的针对孤立有限厚度激波层的最高马赫数动力学线性稳定性计算。
英文摘要
Shock waves in high-speed compressible flows contain finite-thickness, high-gradient regions where the continuum assumption becomes questionable and translational non-equilibrium arises, including non-Maxwellian micro-velocity distributions. Classical shock stability analyses rely on Navier-Stokes or moment closures and cannot retain bi-modal velocity distributions inside the shock. We develop and apply, for the first time, a kinetic linear stability theory (kLST) for one-dimensional normal shocks by linearizing the Boltzmann-BGK equation about kinetic BE-BGK base flows. Perturbations are posed in reduced distribution functions, with macroscopic fields recovered by velocity-space moments, so the stability operator acts on the VDF rather than a closed continuum system. Verified against compressible Couette eigenvalue benchmarks near continuum, the framework is applied to argon shocks at $M_\infty=1.2$, $3.0$, and $4.0$. At low Mach number, where BE-BGK and Gilbarg-Paolucci profiles nearly coincide, the spectra recover stable continuous branches. At higher Mach number, comparing Maxwellian and non-equilibrium VDF-based eigenspectra shows that kinetic effects shift the spectrum toward less stable regions, so continuum predictions can miss important changes even when macroscopic profiles appear well resolved. For large high-Mach matrices--$O(10^5)$ unknowns and up to billions of nonzeros--we develop a parallel SLEPc/PETSc infrastructure using shift-and-invert Arnoldi with MUMPS LU for moderate sizes and Jacobi-Davidson (JD) with block-Jacobi ILU for the largest systems. Coupled spatial/micro-velocity sparsity causes severe LU fill-in, making direct solvers memory-limited and motivating JD. We compute kLST spectra for an $M_\infty=4.0$ shock with 281088 unknowns, to our knowledge the highest-Mach kinetic linear stability calculation reported for isolated finite-thickness shock layers.
Comments65 pages, 19 figures, 17 tables
