Abstract: A new method to simulate flows with patched grids is introduced which is based on second-order Godunov method and Euler equations,and conservation across patch boundaries is satisfied.Using the method,the supersonic flows of bind-rocket and complex flows between two objects are simulated.Computation results are in agreement with experimental data,and describe the complex flows rightly such as the crossing and reflex of shocks.This conservation method with patched grids based on second-order Godunov method and Euler equations is one of effective methods for numerical simulation.