Positivity-preserving strategies and their comparision based on staggered CPR methods

Wang Weizhe; Yan Zhen-Guo; Zhu Huajun; Feng Xinlong

doi:10.7638/kqdlxxb-2024.0170

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Positivity-preserving strategies and their comparision based on staggered CPR methods

更新时间：2026-05-28

- Positivity-preserving strategies and their comparision based on staggered CPR methods
- Vol. 44, Issue 4, Pages: 100-113(2026)
- 作者机构：
  
  1. 新疆大学数学与系统科学学院,乌鲁木齐,830046
  2. 空天飞行空气动力科学与技术全国重点实验室,绵阳,621000
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2024.0170
  CLC： O242.2
- Published：2026
- 稿件说明：
移动端阅览
王伟喆, 燕振国, 朱华君, 等. 交错型CPR方法的保正实现策略及其对比研究[J]. 空气动力学学报, 2026, 44(4): 100−113.

Wang Weizhe, Yan Zhen-Guo, Zhu Huajun, et al. Positivity-preserving strategies and their comparision based on staggered CPR methods[J]. 2026, 44(4): 100-113.
王伟喆, 燕振国, 朱华君, 等. 交错型CPR方法的保正实现策略及其对比研究[J]. 空气动力学学报, 2026, 44(4): 100−113. DOI： 10.7638/kqdlxxb-2024.0170

Wang Weizhe, Yan Zhen-Guo, Zhu Huajun, et al. Positivity-preserving strategies and their comparision based on staggered CPR methods[J]. 2026, 44(4): 100-113. DOI： 10.7638/kqdlxxb-2024.0170.

摘要

计算流体力学方法在模拟涉及强间断、极低密度和极低压力的问题时容易出现因数值误差导致的负密度或负压力，从而导致计算失败，这点对于高阶精度格式尤为突出。为了解决该问题，学界发展了保正限制器，并重点针对其在高阶有限元算法中的应用进行了研究。但是，对于混合CPR/CNNW（correction procedure via reconstruction/compact non-uniform nonlinear weighted）格式，如何保证在从求解点向通量点插值的过程中，通量点上的数值始终满足保正条件，目前仍缺乏深入的研究。本文针对混合CPR/CNNW格式中的通量点保正问题，分别基于保正限制器和一阶迎风插值发展了两种保正策略。理论推导了适用于混合CPR/CNNW格式的平均值保正方法，并设计了在多级RK（multi-stage Runge-Kutta）时间推进中进行平均值保正的方法。在此基础上，对两种保正策略在多种间断问题中的表现进行了数值测试，重点比较两种保正策略的分辨率、鲁棒性和计算效率。数值测试表明，本文提出的保正策略能够有效确保计算不崩溃；其中，fpupwind策略在马赫数2 000射流问题中，将CPU时间降低了约55%，并允许使用更大的时间步长，显著提升了计算效率。

Abstract

High-order accurate algorithms often encounter numerical instabilities

such as negative density or pressure

when simulating flow fields with strong discontinuities

extremely low density

or low pressure. To maintain numerical robustness while preserving high-order accuracy

significant research efforts have been devoted to positivity-preserving limiters

particularly for high-order finite element algorithms. However

existing positivity-preserving limiters predominantly focus on ensuring positivity at solution points instead of flux points. In the hybrid correction procedure via reconstruction/compact non-uniform nonlinear weighted (CPR/CNNW) scheme

there is still a lack of in-depth research regarding the positivity preservation at flux points interpolated from solution points. In this paper

we proposed two positivity-preserving strategies for the hybrid CPR/CNNW scheme using positivity-preserving limiters and a first-order upwind method to enforce positivity constraints at flux points. Furthermore

we developed a positivity-preserving method for cell averages within the hybrid CPR/CNNW scheme

incorporating a multi-stage Runge-Kutta time integration. The two positivity-preserving strategies have been validated by numerical simulations of various problems involving discontinuities

focusing on the resolution

efficiency and robustness of the two strategies. The results show that both strategies can prevent computational crashes. In particular

the fpupwind strategy reduces CPU time by approximately 55% for the Mach 2 000 jet problems

respectively

while allowing for a larger time step size

thereby significantly improving computational efficiency.

关键词

Keywords

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