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利用多小波自适应格式求解流体力学方程
引用本文:孙阳,吴勃英,冯国泰.利用多小波自适应格式求解流体力学方程[J].力学学报,2008,40(6):744.
作者姓名:孙阳  吴勃英  冯国泰
作者单位:哈尔滨工业大学458信箱,推进理论与技术研究所 哈尔滨工业大学理学院数学系 哈尔滨工业大学458信箱,推进理论与技术研究所
摘    要:高阶计算格式的高精度、高分辨率对提高复杂流场的计算水平有重要的意义, 为了提高AUSMPW格式对流场计算中激波等间断的分辨率,减小数值振荡,在原有AUSMPW 格式的基础之上,利用多小波对函数进行多尺度分解,并采取阈值的方法生成自适应网格, 提出了一种新的基于多小波自适应算法的AUSMPW格式,理论上可以达到任意阶精度. 将所得 的压强、密度与原格式、TVD格式及WENO格式的计算结果进行了比较分析. 结果表明改进后 的AUSMPW格式较原格式具有更高的分辨率、更强的捕捉间断的能力及更低的数值耗散.

关 键 词:多小波  自适应  AUSMPW格式  WENO格式  TVD格式  Euler方程
收稿时间:2007-08-03

THE AUSMPW SCHEME BASED ON ADAPTIVE ALGORITHM OF INTERPOLATING MULTIWAVELETS APPLIED TO SOLVE EULER EQUATIONS
Sun Yang , Wu Boying , Feng Guotai.THE AUSMPW SCHEME BASED ON ADAPTIVE ALGORITHM OF INTERPOLATING MULTIWAVELETS APPLIED TO SOLVE EULER EQUATIONS[J].chinese journal of theoretical and applied mechanics,2008,40(6):744.
Authors:Sun Yang  Wu Boying  Feng Guotai
Abstract:The high order precision and high resolution of the high order schemes are very important for complex flow field. In this paper, the new AUSMPW scheme based on adaptive algorithm of interpolating multiwavelets was investigated in order to decrease the numerical oscillation and increase the numerical accuracy for discontinuity, such as shock wave. The interpolating multiwavelets is used for multilevel decomposition of the function, and the method of the valve's value is used to construct adaptive grid. Arbitrary precision can be achieved theoretically. The pressure and density obtained in the algorithm are compared with those from original AUSMPW scheme, TVD scheme and WENO scheme. The numerical results demonstrate that the modified AUSMPW scheme has higher resolution, stronger chaseable ability and lower numerical dissipation.
Keywords:multiwavelets  adaptive  AUSMPW scheme  WENO scheme  TVD scheme  Euler equations  
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