非线性的流体偏微分方程中的激波间断解是物理中很有挑战的问题，其中的Riemann问题可采用解析的方法求出理论解，但采用近似解的方法进行流体动力学数值模拟也可以有效地追踪和捕捉激波.本文以一维激波管为例，对非定常流体基本方程组采用Roe通量差分裂格式，并进行数值模拟.通过与理论解对比，发现其符合度较好.

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.