Abstract: TVD method is especially suitable for the numerical simulation of discontinuous wave of hyperbolic partial differential equations. In this paper, four typical TVD schemes were presented for the numerical simulation of water hammer equations. Through comparison among example calculation, numerical results and theoretical solutions, the differences in numerical performances in aspects of the dissipative and compressible features of different types of TVD schemes were revealed, and TVD schemes were proved to be superior to conventional difference methods. Calculation results in the presence of varying Courant numbers showed that modified Harten’s TVD scheme, TVDMC scheme and full discrete TVD scheme have poor stability in the presence of a wide range of Courant numbers; whereas optimized Sweby’s TVD scheme for water hammer simulation has good stability and high precision.

Key words: high resolution, TVD scheme, numerical simulation, Courant number, water hammer