Abstract: The discontinuous shock wave solution in nonlinear partial differential equations of fluids is a very challenging problem in physics.The Riemann problem can be solved theoretically by analytical method，but the approximate solution method can also be used to track and capture the shock waves effectively in the numerical simulation of fluid dynamics.In this paper，a one-dimensional shock tube is taken as an example，adopting the Roe flux difference splitting scheme to the basic equations of fluid and numerically simulated.It is found that the method is in good agreement with theoretical solution.

Key words: hydrodynamics, Shock wave, Roe flux differential splitting, numerical simulation