Numerical solutions of Euler equations by using a new flux vector splitting scheme
Numerical solutions of Euler equations by using a new flux vector splitting scheme
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DOI：
10.1002/fld.1650170203
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发表时间：
1993-07
影响因子：
1.8
通讯作者：
Gecheng Zha;E. Bilgen
中科院分区：
文献类型：
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作者：
Gecheng Zha;E. Bilgen
本文提出了一种新的矢通量分裂格式。该方案使用垂直于体积界面的速度分量作为特征速度，并在停滞处产生消失的单个质量通量。质量和动量方程的数值耗散也随着马赫数接近零而消失。能量方程的一个扩散项不为零。但对于粘性流动，采用高阶差分可以保证较低的数值扩散。该方案简单易行。该格式已被应用于解决一维（1D）和多维欧拉方程。解是单调的，正激波轮廓是清晰的。对于一维激波管问题，本文格式和Roe格式的计算结果非常接近，与货车Leer格式和Liou-Steffen的平流上游分裂方法（AUSM）的计算结果相比，本文格式和Roe格式的计算结果是最好的。对于多维跨音速流动，得到了尖锐单调的正激波剖面，大多数情况下只有一个过渡区。计算结果与货车Leer格式、AUSM格式及实验结果进行了比较。
A new flux vector splitting scheme has been suggested in this paper. This scheme uses the velocity component normal to the volume interface as the characteristic speed and yields the vanishing individual mass flux at the stagnation. The numerical dissipation for the mass and momentum equations also vanishes with the Mach number approaching zero. One of the diffusive terms of the energy equation does not vanish. But the low numerical diffusion for viscous flows may be ensured by using higher-order differencing. The scheme is very simple and easy to be implemented. The scheme has been applied to solve the one dimensional (1D) and multidimensional Euler equations. The solutions are monotone and the normal shock wave profiles are crisp. For a 1D shock tube problem with the shock and the contact discontinuities, the present scheme and Roe scheme give very similar results, which are the best compared with those from Van Leer scheme and Liou–Steffen's advection upstream splitting method (AUSM) scheme. For the multidimensional transonic flows, the sharp monotone normal shock wave profiles with mostly one transition zone are obtained. The results are compared with those from Van Leer scheme, AUSM and also with the experiment.