Development of a Characteristic Particle Method for Water Hammer Simulation

A characteristic particle method is proposed to simulate a water hammer in piping systems. Two types of regular particles are designed to trace the solution evolution along their corresponding characteristic lines. Besides these regular particles, shock particles with dual states are introduced to follow the shock formed from the amalgamation of characteristic lines. These dual states are derived to satisfy the Rankine-Hugoniot relation across a shock. Particles are implanted in regions without sufficient number to ensure solution accuracy. In this manner, the solution can be accurately resolved both in smooth regions and in those across a shock. The feasibility of the proposed characteristic particle method is validated by numerically solving some test problems and by comparison with the Godunov-type finite volume methods, method of characteristics, or available exact solutions. The computational results demonstrate that the present formulation will be a useful tool to simulate flow transient processes in a piping system.