基于精确Riemann求解器的明满流过渡过程模拟

Preissmann窄缝法模拟明满流过渡过程方法简单，但存在明显的非物理振荡，抑制非物理振荡是该方法应用的关键。基于Godunov格式和精确Riemann求解器对明满流过渡过程进行模拟，针对Riemann问题代数恒等式在明满流交界处不光滑问题，提出了三阶收敛方法与二分法结合的迭代求解方法，保证迭代收敛至真实解；针对由于变量空间重构方法不能准确表达变量在空间中真实物理状态而导致的非物理振荡，提出了基于精确Riemann解的变量空间重构方法，准确表达激波间断在单元内的空间分布状态，从机理上抑制了非物理振荡。实例研究表明，数值计算结果与解析解或实测值吻合良好，研究成果为明满流过渡过程的高精度数值模拟提供了新的方法。

Simulation of transient mixed flows based on the exact Riemann solver

The Preissmann slot method is simple to simulate transient mixed flows, but it has obvious non-physical oscillation. The key to the application of this method is to suppress the non-physical oscillations. The transient mixed flows are simulated based on the Godunov scheme and the exact Riemann solver. In order to solve the problem that the algebraic identity of the Riemann problem is not smooth at the boundary of open and pressure flow, an iterative solution method is proposed. This method combines the third-order convergence method and the dichotomy method to ensure the iterative convergence to the real solution. Considering the fact that the non-physical oscillation caused by the variable space reconstruction method cannot accurately express the real physical state of the variable in space, a variable space reconstruction method based on the exact Riemann solution is proposed. This method can accurately express the spatial distribution state of the shock discontinuity in the cell, and the non-physical oscillation is suppressed from the mechanism. The case study shows that the numerical results are in good agreement with the analytical solutions or the measured values. The research results provide a new method for the high-precision numerical simulation of the transient mixed flows.