AI 中文总结
研究提出用于气体混合物的多物种BGK模型，扩展ESBGK模型，引入相对弛豫目标。提出三种物种弛豫频率方法，在PICLas中实现并经DSMC验证，该模型能再现正确参数，经验弛豫频率与DSMC一致性最佳。
AI 中文摘要
本文提出了一种用于气体混合物的多物种Bhatnagar-Gross-Krook（BGK）模型。该模型根据玻尔兹曼碰撞积分实现了速度、温度和压力张量的正确物种弛豫，以及正确的混合物普朗特数，同时每个物种保留单个弛豫项。通过引入基于Grad 13近似的可变硬球（VHS）生产率导出的每个物种的相对弛豫目标，扩展了椭球统计BGK（ESBGK）模型。提出并分析了三种物种弛豫频率方法：基于Grad 13的每个物种频率、混合物平均频率以及两者的经验调和平均值。该模型在基于粒子的代码PICLas中实现，并针对一系列测试案例与直接模拟蒙特卡罗（DSMC）结果进行了验证，包括0D储层弛豫、质量扩散、超音速库埃特流以及二元和三元气体混合物绕70°钝锥的高超声速流。在所有测试案例中，所提出的模型再现了正确的普朗特数、物种温度、速度弛豫率和压力张量弛豫，经验弛豫频率与DSMC始终具有最佳一致性。
英文摘要
A multi-species Bhatnagar-Gross-Krook (BGK) model for gas mixtures is presented that achieves the correct species-wise relaxation of velocities, temperatures, and pressure tensors according to the Boltzmann collision integral, as well as the correct mixture Prandtl number, while retaining a single relaxation term per species. The model extends the ellipsoidal statistical BGK (ESBGK) model by introducing relative relaxation targets for each species, derived from the Variable Hard Sphere (VHS) production rates of the Grad 13 approximation. Three approaches for the species relaxation frequency are proposed and analyzed: a Grad 13-based per-species frequency, a mixture-averaged frequency, and an empirical harmonic mean of the two. The model is implemented in the particle-based code PICLas and verified against Direct Simulation Monte Carlo (DSMC) results for a range of test cases, including 0D reservoir relaxation, mass diffusion, supersonic Couette flow, and hypersonic flow around a 70° blunted cone for binary and ternary gas mixtures. Across all test cases, the proposed model reproduces the correct Prandtl number, species temperature, velocity relaxation rates and pressure tensor relaxation, with the empirical relaxation frequency consistently yielding the best agreement with DSMC.
