Exact solution of axial liquid-pipe vibration with time-line interpolation

The axial vibration of liquid-pipes, considering the fluid-structure interaction (FSI), can be described by a four-equation model consisting of two equations for the fluid and the other two for the pipe wall. When distributed friction and damping were neglected, the model could be solved with an exact solution developed from the method of characteristics (MOC). The exact solution with a simple recursion process was presented instead of meshing the distance-time plane, introducing no numerical error, while the only weakness was the high time cost. An improved method based on this exact solution is proposed in this work, using the time-line interpolation rather than the recursive algorithm to speed the calculation. As numerical diffusion and oscillation affect the accuracy a lot, various interpolation techniques are investigated and compared. The mean absolute error (MAE) and the structural similarity index measure (SSIM) are employed to assess the accuracy of proposed methods, and the latter was originally developed for the image quality assessment. A hybrid interpolation scheme, mixing the cubic spline and linear interpolation, is proposed and achieves the highest accuracy and the quadratic-linear interpolation is found to be a good choice considering both accuracy and efficiency. The solution method developed here improves the efficiency significantly while retains an acceptable level of the accuracy, especially suitable for the long duration event.