多原子玻尔兹曼碰撞算子的维格纳-埃卡因式分解
Wigner-Eckart Factorization of the Polyatomic Boltzmann Collision Operator
- Eindhoven University of Technology (TU/e)（埃因霍温理工大学）
- Simkinetic
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将维格纳-埃卡因式分解推广到多原子气体的玻尔兹曼碰撞算子，通过SO(3)约化压缩算子并加速计算，经多种基准验证有效。
AI中文摘要：
我们将谱玻尔兹曼碰撞算子的维格纳-埃卡因式分解推广到具有连续内能的多原子气体。由于内能在空间旋转下是不变量，SO(3)约化在博格纳克-拉森能量交换中依然成立，十二维碰撞积分坍缩为九维运动学核心。该核心分解为一个可精确计算的稀疏几何张量，以及一个通过带分数能量耦合辅助拉普拉斯表示的奇异性分辨高斯规则积分的稠密物理张量。该求积法在真实气体的分数指数处达到近机器精度，碰撞不变量被精确嵌入，保留了平动-内能能量交换。该因式分解将算子压缩3至近4个数量级，相比稠密公式加速评估40倍。该方法通过与精确单原子极限、朗道-泰勒弛豫以及解析冻结通道普朗特数对比得到验证，且与已发表的N₂、CO和H₂的同一核校准结果匹配。
英文摘要：
We extend the Wigner-Eckart factorization of the spectral Boltzmann collision operator to polyatomic gases with continuous internal energy. Because internal energies are invariant under spatial rotations, the SO(3) reduction survives the Borgnakke-Larsen energy exchange, and the twelve-dimensional collision integral collapses onto a nine-dimensional kinematic core. The core splits into a sparse geometric tensor, evaluated exactly, and a dense physical tensor, integrated by singularity-resolving Gauss rules with an auxiliary Laplace representation of the fractional energy couplings. The quadrature attains near machine precision at the fractional exponents of real gases. The collision invariants are embedded exactly, preserving the translational-internal energy exchange. The factorization compresses the operator by three to nearly four orders of magnitude and accelerates its evaluation 40-fold over dense formulations. The method is validated against the exact monatomic limit, Landau-Teller relaxation, and an analytic frozen-channel Prandtl number, and it matches a published calibration of the same kernel for N2, CO, and H2.
