基于浅水波理论液体晃动初值问题的数值模拟

针对日益受到关注的液体晃动问题,提出了一种基于浅水波理论的研究方案.该方案采用浅水波理论而非势流理论导出系统控制方程,并通过哈密顿体系表达;利用中心有限差分法和Stormer-Verlet算法进行空间和时间离散;模拟了不同初值条件下的液体晃动情况并对比分析了影响系统非线性响应的主要因素.结果表明,基于浅水波理论能有效解决液体晃动问题;与Euler格式对比,Stormer-Verlet算法精度较高;除共振外对于系统非线性响应的影响容器初始位移比初始速度更显著;非共振情况一定条件下,充液容器运动过程中液体晃动能起到阻尼作用.

Numerical simulation on the initial value problems of liquid sloshing by shallow water wave theory

Based on the shallow water wave theory, a research scheme was proposed for liquid sloshing problems in this paper. In this scheme, the system control equations was derived using the shallow water wave theory rather than potential flow theory, and Hamiltonian system was used to express the equations. The centered finite difference and Stormer-Verlet algorithm were then used for discrete space and time, respectively. Moreover, liquid sloshing under different initial conditions were simulated and compared to obtain the main factor that affecting the nonlinear response of the system. The simulating results indicate that shallow water wave theory can effectively solve the problem of liquid sloshing. Compared with the Eulerian scheme, the Stormer-Verlet scheme had higher accuracy, while compared with the initial velocity of the vehicle, the initial displacement had more remarkable effect on the nonlinearity response of the system. It is also found that under certain conditions, liquid sloshing acted as damping in the process of the vehicle movement.