A characteristic particle method for the Saint Venant equations

A novel characteristic particle method is developed for the Saint Venant equations in the present study. Contrary to the conventional fixed-grid or moving particle methods, the present formulation is built by reallocating the computational particles along the characteristic curves. Both the right- and left-running characteristics are faithfully traced and imitated with their associated computational particles. The annoying numerical nuisance in realizing advection term for the fixed-grid arrangement can be effectively gotten rid of. Besides, special particles with dual states to the enforcement of the Rankine–Hugoniot relation are deliberately imposed to emulate the shock structure. Efficacy of this formulation is verified by solving some benchmark problems with significant transient effects. Computational results are meticulously compared with available analytical solutions. It is concluded that the proposed characteristic particle method will be a useful tool to replicate transient phenomena revealed by the Saint Venant equations.

► Characteristic functions to furnish more physical insights are derived. ► Incorporates characteristic differential equations and Rankine–Hugoniot relation. ► Dual-particle and dual-state particles are employed to resolve the equations. ► Numerical tests on linearized, dam-break and tidal bore problems. ► Yield more accurate results than the existing methods.