两相流中的速度和能量松弛
Velocity and energy relaxation in two-phase flows
AI总结：
本文通过添加松弛项简化六方程两相流模型，在松弛时间趋于零时得到速度和能量趋于一致的两相模型，并讨论了不变区域保持和不可压缩极限。
摘要：
在本研究中，我们解析地研究了双相流中速度和能量松弛的过程。我们首先考虑所谓的六方程两相模型 [Ishii1975, Rovarch2006]。该模型假设每个相拥有自己的速度和能量变量。尽管最近取得了进展，六方程模型在许多实际应用中仍然计算成本高昂。此外，其平流算子可能是非双曲型的，这给构建稳健的数值方案带来了额外的理论困难 [Ghidaglia et al, 2001]。为了简化该系统，我们通过松弛项补充了动量和能量守恒方程。当松弛特征时间趋于零时，速度和能量被约束为趋于两相的公共值。结果，我们得到了一个简单的两相模型，该模型最近被提出用于模拟剧烈充气流动 [Dias et al, 2010]。还讨论了简化模型的不变区域保持和不可压缩极限。最后，给出了几个数值结果。
英文摘要：
In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model assumes each phase to possess its own velocity and energy variables. Despite recent advances, the six equations model remains computationally expensive for many practical applications. Moreover, its advection operator may be non-hyperbolic which poses additional theoretical difficulties to construct robust numerical schemes |Ghidaglia et al, 2001]. In order to simplify this system, we complete momentum and energy conservation equations by relaxation terms. When relaxation characteristic time tends to zero, velocities and energies are constrained to tend to common values for both phases. As a result, we obtain a simple two-phase model which was recently proposed for simulation of violent aerated flows [Dias et al, 2010]. The preservation of invariant regions and incompressible limit of the simplified model are also discussed. Finally, several numerical results are presented.
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