| 引用本文: | 张怀宝,王光学,王靖宇.原始变量守恒形式控制方程的时间准确性分析.[J].国防科技大学学报,2019,41(2):37-43.[点击复制] |
| ZHANG Huaibao,WANG Guangxue,WANG Jingyu.Time accuracy analysis of primitive variable-based conservative form governing equations[J].Journal of National University of Defense Technology,2019,41(2):37-43[点击复制] |
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| 原始变量守恒形式控制方程的时间准确性分析 |
| 张怀宝, 王光学, 王靖宇 |
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(中山大学 物理学院， 广东 广州 510006)
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| 摘要: |
| 基于压力、速度和温度的原始变量为自变量的守恒形式的控制方程可应用于定常流动问题，但是在求解非定常问题，例如某一典型激波管问题时，激波后温度出现过冲现象，即使通过细化网格、提高空间格式精度或者换用其他通量格式仍不能消除，这表明误差可能来自该方法本身。采用一维Euler方程对该方法进行数值分析。分析结果表明，数值误差来自时间项。通过构造相应的双时间步方程，虚拟时间项采用原始变量，而物理时间项采用守恒变量，并在两个相邻物理时间步内作为定常问题求解，可以收敛到相应的守恒形式，消除上述误差，得到准确的非定常数值解。 |
| 关键词: 原始变量 守恒律 激波管问题 计算流体力学 双时间步 |
| DOI：10.11887/j.cn.201902006 |
| 投稿日期：2018-02-28 |
| 基金项目:国家部委基金资助项目（41406030101） |
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| Time accuracy analysis of primitive variable-based conservative form governing equations |
| ZHANG Huaibao, WANG Guangxue, WANG Jingyu |
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(School of Physics, Sun Yat-sen University, Guangzhou 510006, China)
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| Abstract: |
| The governing equations using primitive properties of pressure, velocity and temperature as dependent variables, but constructed in the conservative form can be applied for calculating solutions for steady state problems. When the method was recently used to simulate a canonical shock-tube problem, however, overshoot of temperature was observed after the shock. Moreover, the errors cannot be eliminated by using fine grid, high spatial order of accuracy or any alternative inviscid fluxes schemes that are available, implying the numerical discrepancy may be caused by the method itself. Numerical analysis was conducted on the method using the one-dimensional Euler equations as the model equation system. It can be shown that the numerical error specifically arises from the discretized time terms. A dual-time-looping technique was developed to address the issue. It used conservative variables in physical-time derivatives while primitive variables for pseudo-time terms. An inner iteration procedure within two adjacent physical-time steps were driven until a steady state was reached. The resulting governing equation converged to the corresponding conservative form in time, and the time-accurate solution was recovered. |
| Keywords: primitive variables conservation law shock-tube problem computational fluid dynamics dual-time-looping |
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