Time-marching Method for Complicated Compressible Flow Equations with Source Term
Time-marching Method for Complicated Compressible Flow Equations with Source Term
复制标题
带源项的复杂可压缩流动方程的时间推进方法
DOI：
10.1007/978-3-642-56535-9_17
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
S. Yamamoto
中科院分区：
文献类型：
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作者：
S. Yamamoto
本文提出了一种时间推进法，用于同时求解可压缩流动方程和附加的复杂物理基本方程，如热化学非平衡、非平衡凝聚和磁等离子体动力学（MPD）。高超声速热化学非平衡流动可以同时求解化学组分连续性方程、动量方程、总能量方程和振动能量方程。在这些方程的源项中模拟了化学反应和振动能的弛豫。本课题组提出了一种求解高超声速热化学非平衡流的高分辨率方法[1]。还成功地计算了具有热化学非平衡效应的非定常IV型激波干扰流[2]。本文用求解气、液相流动方程的方法计算了跨音速非平衡凝结流动。在大多数情况下，欧拉方程是用时间推进法求解的，而非平衡湿蒸汽气体是通过积分液滴沿着各流线的生长来近似的。因此，很难同时使用时间推进法求解所有方程。轴对称磁等离子体动力学流动一般是通过求解由麦克斯韦方程和欧姆定律导出的等离子体流动方程和磁感应强度方程来计算的。现有的方法大多将磁感应强度方程作为椭圆型方程单独用松弛法求解。其原因可能是磁场的特征时间比流场的特征时间短得多。
Time-marching methods for simultaneously solving compressible flow equations and additional fundamental equations of complicated physics, such as therrnochemical nonequilibrium, nonequilibrium condensation, and magnet-plasma dynamics(MPD), are presented. Hypersonic thermochemical nonequilibrium flows can be simulated solving continuity equations of chemical species, momentum equations, a total energy equation, and a vibrational energy equation simultaneously. Chemical reactions and the relaxation of vibrational energy are modeled in the source term of those equations. Our research group proposed a high-resolution method for solving hypersonic thermochemical nonequilibrium flows[1]. Unsteady Type IV shock interference flows with thermochemical nonequilibrium effects were successfully calculated, too[2]. Transonic flows with nonequilibrium condensation have been calculated solving flow equations for gas and liquid phases. In most of them, the Euler equations are solved using the timemarching method, while the nonequilibrium wet-steam gas is approximated integrating the growth of droplet along each streamline. Therefore, it is difficult to solve all equations simultaneously using the time-marching method. Axisymmetric MPD flows have been generally calculated solving plasma flow equations and the equation of magnetic induction derived from the Maxwell’s equations and the Ohm’s law. In most of existing methods, the equation of magnetic induction was solved separately by a relaxation method as an elliptic equation. The reason may be that the characteristic time of magnetic field is much shorter than that of flow field.