SCAA colloquium: Teke Xu

Title: A non-linear model for the water hammer problem

 

Abstract: The water flow and water hammer in a pipe is usually modelled by Euler equations which consists of 2 partial differential equations. The classical PDEs are nonlinear and inhomogeneous, and according to the existing research so far, it can be simplified to a switched DAE or ODE system under some assumptions. The result in some literature shows that simplification works well and converges to the PDE model by numerical solutions. However, how they (PDE and ODE model) converge to each other in an analytical way, or the error between them has not been quantified, and my work is to close this gap. The main method is to divide the process into 3 parts: before the valve closes, when the valve closes and after the valve has been closed.