Abstract: The Preissmann slot method is simple to simulate transient mixed flows, but it has obvious non-physical oscillation. The key to the application of this method is to suppress the non-physical oscillations. The transient mixed flows are simulated based on the Godunov scheme and the exact Riemann solver. In order to solve the problem that the algebraic identity of the Riemann problem is not smooth at the boundary of open and pressure flow, an iterative solution method is proposed. This method combines the third-order convergence method and the dichotomy method to ensure the iterative convergence to the real solution. Considering the fact that the non-physical oscillation caused by the variable space reconstruction method cannot accurately express the real physical state of the variable in space, a variable space reconstruction method based on the exact Riemann solution is proposed. This method can accurately express the spatial distribution state of the shock discontinuity in the cell, and the non-physical oscillation is suppressed from the mechanism. The case study shows that the numerical results are in good agreement with the analytical solutions or the measured values. The research results provide a new method for the high-precision numerical simulation of the transient mixed flows.