发表机构
Fondazione Istituto Italiano di Tecnologia; Center for Life Nano-Neuroscience at la Sapienza; Istituto per le Applicazioni del Calcolo “Mauro Picone; Italian National Research Council（意大利理工大学基金会; 罗马一大生命纳米神经科学中心; 毛罗·皮科内计算应用研究所; 意大利国家研究委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二阶卡尔曼截断在稳态流动模拟中的适用性，发现其能准确捕捉低雷诺数准线性动力学，但在雷诺数约20的复杂涡结构稳态中失效，并指出闭合方案或变量变换可能改善收敛。
AI 中文摘要
研究表明，二阶卡尔曼截断（C2）在强迫参数低于临界值1/2时，能以二阶精度捕捉衰减强迫逻辑斯蒂方程的稳态。随后，我们通过二维周期强迫流的卡尔曼格子玻尔兹曼模拟，研究了这些结果向空间扩展系统的推广。发现C2能正确再现低雷诺数（1至10之间）的准线性动力学，该范围远高于强迫逻辑斯蒂方程的临界值。然而，对于雷诺数约为20时以持续涡结构为特征的更复杂稳态，C2无法捕捉。有趣的是，后者观察到的发散与增长逻辑斯蒂C2线性化的失控行为具有定性相似性，这表明适当的闭合方案和/或变量变换可能改善C2过程的收敛性。
英文摘要
It is shown that the second-order Carleman truncation (C2) captures the steady state of the decaying forced logistic with second-order accuracy in the forcing parameter, provided such forcing remains below a critical value of 1/2. We then investigate the extension of these results to spatially extended systems by means of Carleman Lattice Boltzmann simulations of a two-dimensional periodically forced flow. It is found that C2 correctly reproduces the low-Reynolds-number (between 1 and 10) quasi-linear dynamics, well above the critical value of the forced logistic equation. However, C2 fails to capture more complex steady states characterised by persistent vortical structures at Reynolds numbers around 20. Interestingly, the divergence observed in the latter case shows qualitative similarities with the runaway behaviour of the C2 linearization of the growing logistics, suggesting that suitable closures and/or change of variables may improve the convergence of the C2 procedure.
Comments12 pages, 9 figures
