Chebyshev super spectral viscosity method for water hammer analysis

In this paper, a new fast and efficient algorithm, Chebyshev super spectral viscosity (SSV) method, is introduced to solve the water hammer equations. Compared with standard spectral method, the method's advantage essentially consists in adding a super spectral viscosity to the equations for the high wave numbers of the numerical solution. It can stabilize the numerical oscillation (Gibbs phenomenon) and improve the computational efficiency while discontinuities appear in the solution. Results obtained from the Chebyshev super spectral viscosity method exhibit greater consistency with conventional water hammer calculations. It shows that this new numerical method offers an alternative way to investigate the behavior of the water hammer in propellant pipelines.