利用多小波自适应格式求解流体力学方程

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. 

THE AUSMPW SCHEME BASED ON ADAPTIVE ALGORITHM OF INTERPOLATING MULTIWAVELETS APPLIED TO SOLVE EULER EQUATIONS

The high order precision and high resolution of the highorder schemes are very important for complex flow field. In this paper, thenew AUSMPW scheme based on adaptive algorithm of interpolating multiwaveletswas investigated in order to decrease the numerical oscillation and increasethe numerical accuracy for discontinuity, such as shock wave. Theinterpolating multiwavelets is used for multilevel decomposition of thefunction, and the method of the valve's value is used to construct adaptivegrid. Arbitrary precision can be achieved theoretically. The pressure anddensity obtained in the algorithm are compared with those from originalAUSMPW scheme, TVD scheme and WENO scheme. The numerical results demonstratethat the modified AUSMPW scheme has higher resolution, stronger chaseableability and lower numerical dissipation.