基于有限体积法Godunov格式的水锤计算模型

针对管道内水锤问题,基于一阶和二阶Godunov格式的有限体积法建立数学模型并进行模拟分析。采用Riemann求解器对离散通量进行求解,同时在计算中引入对流项;采用MUSCL-Hancock方法进行重构得到二阶精度的Godunov格式,为了避免虚假振荡引入MINMOD斜率限制器;提出了虚拟边界的处理方法,实现了计算区域的所有节点和边界的统一计算。计算分析表明,虚拟边界法既保证了计算结果的精确性,又避免了边界处理的复杂性;一阶Godunov格式与传统的特征线法计算结果一致;当库朗特数小于1时,一阶Godunov格式和特征线法的瞬变压力可能出现严重的数值耗散,但二阶Godunov格式可有效抑制数值衰减从而得到更为准确稳定的计算结果;在马赫数很小的情况下,对流项对模拟结果的影响可忽略。

Water hammer model based on finite volume method and Godunov-type scheme

Finite volume method with first order and second order Godunov schemes is presented to simulate and analyze the water hammer problem. Firstly, the Riemann solver is used to solve the discrete flux and the convection term is considered. MUSCL-Hancock method is used to reconstruct the second order precision Godunov scheme, while the MINMOD slope limiter is introduced to avoid spurious oscillations. The virtual boundary method is proposed to deal with the boundary calculations, which can realize a unified calculation scheme for all the nodes inside the computational domain and at the boundaries. Analysis shows that the virtual boundary method can ensure the accuracy of the calculation results, and it can also avoid the complexity of the boundary computation. The results predicted by the first-order Godunov scheme are identical with those from the Method of Characteristics(MOC). When the Courant number is less than one, the transient pressure calculated from the first-order Godunov scheme and the MOC scheme may appear serious numerical dissipation. However, the second-order Godunov scheme can effectively suppress numerical attenuation and obtain more accurate and stable results. In the cases with a low Maher number, the convection term can be neglected in simulations.