Abstract In this paper, a Roe-type Riemann solver is developed for the two-fluid seven-equation model. The general form of equations of state (EOS) is under consideration in order to simulate water-steam flow. To avoid the difficulty of mathematical treatment, the governing equations system is transformed into a equations system in which the primary variables are density, velocity, entropy and phase volume fraction, and it is solved by the weak formulation of Roe scheme because the equations system is non-conservative. The equations system is approximated by a linear equations system with an averaged matrix. The averaged matrix satisfies hyperbolicity condition, consistency condition and generalised jump condition, and the expression of the averaged matrix is obtained by integrating along a specific path. Due to the general EOS, the calculation of the averaged matrix, eigenvalues and eigenvectors is complex, and some variables are calculated by numerical integration method. The solver is tested by the two-phase flow benchmarks which have exact solution. The numerical results are in agreement with the exact solution, and the prediction of the smooth solution performs better than that of the shock solution. The prediction of the shock is not accurate, because the transformation of equations system changes shock’s condition and it forces the entropy to remain constant unphysically. The solver is also tested by the cases with the tubulated EOS and IAPWS-IF97. It performs well and has the ability to simulate the fluid with complex EOS.

中文翻译：

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用于二流体七方程模型的黎曼求解器的开发

摘要 本文针对二流体七方程模型开发了一种Roe型黎曼求解器。状态方程 (EOS) 的一般形式正在考虑中，以模拟水蒸汽流动。为避免数学处理的困难，将控制方程组转化为主要变量为密度、速度、熵和相体积分数的方程组，并用Roe格式的弱公式求解，因为方程组为不保守。方程组近似为具有平均矩阵的线性方程组。平均矩阵满足双曲条件、一致性条件和广义跳跃条件，平均矩阵的表达式是沿特定路径积分得到的。由于一般的EOS，平均矩阵、特征值和特征向量的计算比较复杂，部分变量采用数值积分方法计算。求解器通过具有精确解的两相流基准测试。数值结果与精确解一致，平滑解的预测效果优于冲击解的预测。对激波的预测是不准确的，因为方程组的变换改变了激波的条件，迫使熵非物理地保持恒定。求解器还通过带有管状 EOS 和 IAPWS-IF97 的案例进行测试。它表现良好，能够模拟具有复杂EOS的流体。求解器通过具有精确解的两相流基准测试。数值结果与精确解一致，平滑解的预测效果优于冲击解的预测。对激波的预测是不准确的，因为方程组的变换改变了激波的条件，迫使熵非物理地保持恒定。求解器还通过带有管状 EOS 和 IAPWS-IF97 的案例进行测试。它表现良好，能够模拟具有复杂EOS的流体。求解器通过具有精确解的两相流基准测试。数值结果与精确解一致，平滑解的预测效果优于冲击解的预测。对激波的预测是不准确的，因为方程组的变换改变了激波的条件，迫使熵非物理地保持恒定。求解器还通过带有管状 EOS 和 IAPWS-IF97 的案例进行测试。它表现良好，能够模拟具有复杂EOS的流体。因为方程组的变换改变了激波的条件，迫使熵在物理上保持不变。求解器还通过带有管状 EOS 和 IAPWS-IF97 的案例进行测试。它表现良好，能够模拟具有复杂EOS的流体。因为方程组的变换改变了激波的条件，迫使熵在物理上保持不变。求解器还通过带有管状 EOS 和 IAPWS-IF97 的案例进行测试。它表现良好，能够模拟具有复杂EOS的流体。