| 基于特征线方程N—S方程非增量型分离算法 |
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| 引用本文： | 陈炎,曹树良,梁开洪,祝宝山.基于特征线方程N—S方程非增量型分离算法[J].排灌机械,2009,27(5):327-331. |
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| 作者姓名： | 陈炎 曹树良 梁开洪 祝宝山 |
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| 作者单位： | 清华大学,热能工程系,水沙科学与水利水电工程国家重点实验室,北京,100084 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 为克服传统有限元方法求解流场时由于对流项占优而引起的求解振荡和基函数选择困难的问题,推导了基于特征线方程的粘性不可压N-S方程的增量型和非增量型分离算法的公式及求解步骤,并讨论了两者的Babuska-Brezzi条件.沿着特征线方向,N-S方程的对流项消失,方程矩阵是自伴随矩阵,可以自动满足有限单元法中能量泛函最小的要求,并可以给出合理的粘性耗散项.动量方程的求解采用非增量型分离算法,压力和速度可以采用任意阶次的插值函数,离散后的方程自动满足Babuska-Brezzi条件.为验证算法的可靠性,采用T3P3空间等阶次U-p单元计算了方柱绕流.结果表明：基于特征线方程的非增量型分离算法可以很好地应用于粘性不可压流场的计算,与目前流行的其它方法相比,该算法有明显的优势.
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| 关 键 词： | 分离算法 计算流体力学 有限元方法 特征线方程 Babuska—Brezzi条件 方柱绕流 |
Numerical study on characteristics based on non incremental split scheme |
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| Chen Yan,Cao Shuliang,Liang Kaihong,Zhu Baoshan.Numerical study on characteristics based on non incremental split scheme[J].Drainage and Irrigation Machinery,2009,27(5):327-331. |
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| Authors: | Chen Yan Cao Shuliang Liang Kaihong Zhu Baoshan |
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| Institution: | (Key Laboratory for River Dynamics and Hydraulic Engineering, Department of Thermal Engineering. Tsinghua University, Beijing 100084, China) |
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| Abstract: | The formula and solution procedure of characteristics based on incremental and non-incremental split scheme are given in this paper, and the Babuska-Brezzi condition of the two schemes is discussed. The convective acceleration term disappears along the characteristic. The momentum equation is solved by non-incremental split method, which satisfies the Babuska-Brezzi condition. Thus there is no restriction on the nature of the interpolation function. At last T3P3 element is used to solve incompressible N- S equation. The result shows that the characteristics based on non-incremental split scheme has good performance. |
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| Keywords: | split method computational fluid dynamics FEM characteristic equation Babuska-Brezzi condition flow around square cylinder |
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