Efficient Quasi-Two-Dimensional Water Hammer Model on a Characteristic Grid

This note proposes a new quasi-two-dimensional (quasi-2D) numerical scheme for simulating a water hammer that significantly reduces the computational burden compared to two existing quasi-2D schemes, as numerically demonstrated in this note by application to a reservoir-pipe-valve system. Computational cost is decreased through using one-dimensional (1D), rather than two-dimensional equations for pressure head and discharge and using a staggered grid with half of the computational nodes compared to a rectangular grid. It is valid to use the proposed 1D characteristic equations for the pressure head and discharge, as it is proved that these yield identical results to explicit quasi-2D solution procedures previously introduced in the literature.