无粘可压缩流动的改进高精度方法

为更准确捕捉复杂流场的流动细节,通过对WENO格式的光滑因子进行改进,发展了一种新的五阶WENO格式。对三阶ENO格式进行加权可以得到五阶WENO格式,但是不同的加权处理,WENO格式在极值处保持加权基本无振荡的效果不同,本文构造了二阶精度的局部光滑因子,及不含一阶二阶导数的高阶全局光滑因子,从而实现WENO格式在极值处有五阶精度。基于改进五阶WENO格式,对一维对流方程、一维和二维可压缩无粘问题进行算例验证,并与传统WENO-JS格式和WENO-Z格式进行比较。计算结果表明,改进五阶WENO格式有较高的精度和收敛速度,有较低的数值耗散,能有效捕捉间断、激波和涡等复杂流动。

One improved high accuracy scheme for compressible inviscid flow computation

For more accurately capturing complex flows,a new fifth-order WENO scheme is developed by improving the smoothing factor of WENO scheme. Weighting the third-order ENO scheme can lead to a fifth-order WENO scheme,but with different weighting methods,the WENO scheme will have different effects of maintaining weighted essentially non-oscillatory schemes at extreme values. In this paper,the local smoothing factor of second-order accuracy and the high-order global smoothing factor without first-order or second-order derivative are constructed,so that the WENO scheme has fifth-order accuracy at the extreme values.Based on the improved fifth-order WENO scheme,the classical problems of one-dimensional convection equations,one-dimensional and two-dimensional Euler equations are verified by examples,and compared with the traditional WENO-JS scheme and WENO-Z scheme.The calculation results show that the improved fifth-order WENO scheme has higher accuracy and convergence speed,and can effectively capture complex flows such as discontinuities,shock waves and eddies with low dissipation.