Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model
Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model
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DOI：
10.1016/j.rinp.2017.12.044
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发表时间：
2018-03
影响因子：
5.3
通讯作者：
M. R. Saleem;Ishtiaq Ali;Shamsul Qamar
中科院分区：
文献类型：
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作者：
M. R. Saleem;Ishtiaq Ali;Shamsul Qamar
本文对一种简化的五方程两相流模型进行了数值研究。模型的建立基于守恒定律和能量交换定律。该模型是非保守的，控制方程包含两个质量守恒方程，一个是总动量守恒方程，一个是总能量守恒方程。第五个方程是两个相中的一个的能量方程，它在右边包含一个源项，用于以机械和热力学功的形式结合两种流体之间的能量交换。采用Runge-Kutta间断Galerkin有限元方法求解模型方程。该方法的主要特点包括形式上的高阶精度、非线性稳定性、处理复杂几何形状的能力以及在不产生虚假振荡的情况下捕捉解中的尖锐不连续性或强梯度的能力。该方法具有较强的鲁棒性，适用于大规模的时变计算问题。文中给出了几个两相流的算例。为了验证和比较结果，还使用交错中心格式求解相同的模型方程。结果表明，与交错中心格式相比，间断Galerkin格式具有更好的计算结果。
In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.