AI 中文总结
本文针对确定性多尺度气体流模拟的维度灾难，提出基于子问题集与随机离散速度的SDV-DUGKS方法，可节省超80%内存且精度相当，为工程应用提供了潜力。
AI 中文摘要
确定性多尺度气体流模拟长期受维度灾难困扰：离散速度数量随速度空间维度和马赫数急剧增长，耗尽可用内存与计算资源。为解决该问题，本文提出一种基于子问题集（ensemble-of-subproblems）策略的内存高效确定性方法，采用随机离散速度。该策略将原本计算成本高昂的问题转化为一系列可独立高效求解的子问题。具体而言，所提方法用多个小型随机速度集替代传统大型确定性速度集，每个随机速度集定义一个子问题，该子问题通过确定性多尺度数值格式求解，该格式通过蒙特卡洛积分计算宏观矩，最终流场由所有子问题的算术平均得到。本研究采用离散统一气体动理学格式（DUGKS）进行空间离散，将所得方法命名为SDV-DUGKS。为验证所提方法，开展多个数值测试案例，包括：（a）一维激波结构；（b）二维腔流；（c）绕方柱的超声速流。一维激波结构的结果证实了所提方法的可行性，二维案例表明，与确定性对应方法相比，所提方法节省超过80%的内存使用，同时保持相当的精度。这些结果表明，所提方法显著降低了多尺度流模拟的内存需求，在缓解维度灾难方面展现出强大潜力，该维度灾难目前阻碍着确定性多尺度数值格式应用于工程问题。
英文摘要
Deterministic multiscale gas flow simulations have long suffered from the curse of dimensionality: the number of discrete velocities increases dramatically with the velocity space dimension and the Mach number, exhausting available memory and computational resources. To address this issue, this paper proposes a memory-efficient deterministic method based on an ensemble-of-subproblems strategy using stochastic discrete velocities. This strategy transforms the originally computationally expensive problem into a series of independently and efficiently solvable subproblems. To be concrete, the proposed method replaces the conventional large deterministic velocity set with multiple small random velocity sets. Each random set defines a subproblem, which is solved by a deterministic multiscale numerical scheme that computes macroscopic moments via Monte Carlo integration. The final flow field is obtained by arithmetic averaging over all sub-problems. In this work, we employ the discrete unified gas kinetic scheme (DUGKS) for spatial discretization and term the resulting method SDV-DUGKS. To validate the proposed method, several numerical test cases are conducted, including (a) the one-dimensional shock structure, (b) the two-dimensional cavity flow, and (c) supersonic flow around a square cylinder. The results of the one-dimensional shock structure confirm the feasibility of the proposed method. The two-dimensional cases demonstrate that, compared to its deterministic counterpart, the proposed method saves more than 80% of memory usage while maintaining comparable accuracy. These results indicate that the proposed method markedly reduces memory demand for multiscale flow simulations and exhibits strong potential to alleviate the curse of dimensionality that currently hinders deterministic multiscale numerical schemes from being applied to engineering problems.
Comments27 pages, 31 figures
