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 引用本文: 曹云, 周领, 方浩宇, 车同川. 输水管道水锤与流固耦合5阶有限体积法模型. 力学学报, 2023, 55(8): 1637-1648.
Cao Yun, Zhou Ling, Fang Haoyu, Che Tongchuan. Fifth-order finite volume models of water hammer and fluid-structure interaction in pipes. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(8): 1637-1648.
 Citation: Cao Yun, Zhou Ling, Fang Haoyu, Che Tongchuan. Fifth-order finite volume models of water hammer and fluid-structure interaction in pipes. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(8): 1637-1648.

## FIFTH-ORDER FINITE VOLUME MODELS OF WATER HAMMER AND FLUID-STRUCTURE INTERACTION IN PIPES

• 摘要: 针对输水管道水锤与流固耦合瞬变流现象, 采用有限体积5阶精度WENO/MWENO求解格式进行建模和模拟研究. 在水锤和流固耦合基本控制方程中引入动态摩阻, 并在流固耦合模型中考虑管道径向形变的影响, 采用5阶WENO/MWENO格式求解. 提出三虚拟边界单元法进行边界条件计算, 既保证边界单元体精度达到5阶精度, 同时又简化计算过程; 采用具有3阶时空精度的龙格−库塔法进行时间积分, 保证时步迭代过程中的计算精度. 将本文所建模型计算结果与已有模型解析解进行对比, 分析5阶有限体积法模型的计算精度和效率. 结果表明: 文章模型具有较高的适用性, 其能更好地模拟输水管道水锤与流固耦合的瞬时压力波动, 有效避免模拟结果出现虚假数值振荡; 与2阶模型相比, 5阶模型具有更高的计算精度和效率.

Abstract: Finite volume method with fifth-order WENO/MWENO scheme is developed to simulate water hammer and fluid-structure interaction (FSI) in pipes. The unsteady friction is introduced into the water hammer and FSI governing equations, the radial deformation is considered in FSI model, fifth-order WENO/MWENO scheme is used to solve the equations. A triple virtual boundary method is proposed to deal with the boundary calculations, the method simplifies the calculation process and keep the precision of the boundary element in fifth-order; third-order Runge-Kutta method is adopted for time integration to maintain the calculation precision. The calculation results of the established models are compared with exact solutions, and the accuracy and efficiency of the fifth-order models are analyzed. Results show that the proposed models have high applicability, they can better simulate the water hammer and FSI pressures in pipes, and can effectively avoid numerical oscillation; compared with the second-order models, the fifth-order models have higher computational accuracy and efficiency.

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