Abstract: The RKDG finite element method, Level Set method and modified Ghost Fluid method with Isentropic fix are used to simulate a one-dimensional compressible multicomponent Euler equation. A third-order accurate RKDG finite element method is used to solve the Euler equation, the Level Set equation and the re-initiation equation. Numerical tests on one-dimensional compressible two-fluid flows are made and satisfactory results are obtained.