A Lagrangian particle model for one-dimensional transient pipe flow with moving boundary

For simulating fluid transients in pipelines with moving water-air interface, a one-dimensional Lagrangian particle model with second-order accuracy in both space and time is proposed. In this model, the meshless smoothed particle hydrodynamics (SPH) is used to approximate the spatial derivatives in the waterhammer equations, and the symplectic leap frog scheme is used for time integration. The nonlinear convective terms–which are mostly neglected in classical water hammer–are taken into account. The details of the Lagrangian particle method, boundary condition treatment and artificial viscosity for remedy of numerical oscillations due to shocks are presented. Two typical cases including transient flow with entrapped air pocket and rapid pipe filling are simulated and the results are validated against available experimental and numerical solutions, which has wide applications for flow simulation in drainage networks. To test the shock capturing ability of the developed model, the classical water hammer problem is also simulated and good agreement with the theoretical solution is obtained. It is shown that the proposed Lagrangian particle model is capable of solving waterhammer equations with moving boundaries and that it has high potential for multiphase transient flows.