Unsteady nonlinear coupled constitutive relations model based on the PHengLEI framework

Yang Junyuan; Zeng Shuhua; Zhao Wenwen; Zhang Yanlan; An Jiaqi; Sun Ao; Chen Weifang

doi:10.7638/kqdlxxb-2025.0225

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Unsteady nonlinear coupled constitutive relations model based on the PHengLEI framework

更新时间：2026-05-28

- Unsteady nonlinear coupled constitutive relations model based on the PHengLEI framework
- Vol. 44, Issue 3, Pages: 155-165(2026)
- 作者机构：
  
  浙江大学航空航天学院,杭州,310027
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2025.0225
  CLC： V211.3
- Published：2026
- 稿件说明：
移动端阅览
杨俊沅, 曾舒华, 赵文文, 等. 基于风雷软件的非定常非线性耦合本构关系模型[J]. 空气动力学学报, 2026, 44(3): 155−165.

Yang Junyuan, Zeng Shuhua, Zhao Wenwen, et al. Unsteady nonlinear coupled constitutive relations model based on the PHengLEI framework[J]. 2026, 44(3): 155-165.
杨俊沅, 曾舒华, 赵文文, 等. 基于风雷软件的非定常非线性耦合本构关系模型[J]. 空气动力学学报, 2026, 44(3): 155−165. DOI： 10.7638/kqdlxxb-2025.0225

Yang Junyuan, Zeng Shuhua, Zhao Wenwen, et al. Unsteady nonlinear coupled constitutive relations model based on the PHengLEI framework[J]. 2026, 44(3): 155-165. DOI： 10.7638/kqdlxxb-2025.0225.

摘要

为实现跨流域非平衡流动的高效模拟，本文基于国家数值风洞的风雷（PHengLEI）开源框架，设计开发了非线性耦合本构关系（nonlinear coupled constitutive relations

NCCR）模型求解器PHengLEI-NCCR，并进一步构建了非定常非线性耦合本构关系模型（ALE-NCCR）。新模型有效拓展了风雷软件在连续-稀薄跨流域流动中的计算能力和适用范围，并对其在典型算例中的计算准确性进行了系统验证。首先给出了PHengLEI-NCCR求解器中涉及的控制方程、无量纲化和迭代计算策略。随后，通过ALE-NCCR求解器计算了HBS （hyper ballistic shape）模型的俯仰振荡的静、动导数。结果表明：在连续流域， PHengLEI-NCCR求解器的计算结果与实验数据具有良好一致性；在稀薄流域，PHengLEI-NCCR求解器较传统的纳维-斯托克斯-傅里叶（Navier–Stokes–Fourier

NSF）方程能够更准确地捕捉非平衡效应，与DSMC结果更为接近。此外，ALE-NCCR模型在连续流条件下可回归于ALE-NSF方程的时间精度与物理可靠性，充分证明了新模型的跨流域适用性与非定常动边界模拟能力。

Abstract

To enable efficient prediction of rarefied nonequilibrium effects

a nonlinear coupled constitutive relations (NCCR) solver and an unsteady NCCR solver (ALE-NCCR) were developed within the open source PHengLEI framework of the National Numerical Wind Tunnel project. The proposed models substantially extend the capability and applicability of PHengLEI for continuum–rarefied cross-regime flows

and their accuracy has been systematically validated through a series of representative test cases. The governing equations

non-dimensionalization procedures

and inner iteration strategies adopted in the PHengLEI-NCCR solver are first presented. The dual-time stepping ALE-NCCR model is then applied to compute the static and dynamic derivatives of the HBS configuration undergoing pitching oscillations. Numerical results show that the NCCR model exhibits strong agreement with experimental data in continuum regimes and provides substantially improved accuracy compared with the Navier–Stokes–Fourier (NSF) equations in rarefied nonequilibrium regimes

approaching the fidelity of DSMC simulations. Furthermore

the ALE-NCCR model recovers the accuracy of the ALE-NSF equations for unsteady continuum flows. These results demonstrate the robustness

accuracy

and broad applicability of the proposed NCCR based solvers.

关键词

Keywords

references

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