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应用特征线差分法求解耦合瞬变问题时存在难以避免的多波插值问题,会引入较大的插值误差。为了解决此问题,本文提出了一种求解管道耦合水力瞬变模型的Godunov计算格式。首先基于有限体积法对模型进行数值离散,然后采用时空均为二阶精度的三步MUSCL-Hancock方法计算单元界面上的数值通量,同时引入斜率限制器函数来抑制虚假的数值振荡。在计算边界单元时,采用Rankine-Hugoniot条件与边界条件相结合的方法建立边界方程,有效降低了计算的复杂程度。实验与仿真对比表明:本文的计算结果与实验结果吻合较好,激波捕捉准确且无虚假的数值振荡,进而证明了该方法的可行性和有效性。
There are some inevitable problems of multi-wave interpolation when solving the coupling transient problem by using the characteristic-line difference method, which leads to a large interpolation error. In order to solve this problem, this paper presents a Godunov calculation formula for solving the pipeline coupled hydraulic transient model. Firstly, the model is numerically discretized based on the finite volume method, and then the three-step MUSCL-Hancock method with space-time accuracy is used to calculate the numerical flux at the cell interface. The slope limiter function is introduced to suppress the false numerical oscillation. In the calculation of boundary elements, the boundary equation is established by combining Rankine-Hugoniot conditions with the boundary conditions, which effectively reduces the computational complexity. The comparison of experiment and simulation shows that the calculation results in this paper are in good agreement with the experimental ones, and the shock waves capture accurate and unscented numerical oscillations, which proves the feasibility and effectiveness of this method.