Abstract: Flames and inert gases past an cylinder obstacle were numerically simulated by using the immersed boundary method used in the 3D compressible viscous flow and the high-order accurate total variation diminishing (TVD) schemes based on the high-order piecewise parabolic method (PPM). In the turbulent calculation, the large eddy simulation (LES) was introduced and the eddy break-up(EBU) model was adopted to compute the chemical reaction rate. Comparison of the simulated and experimental results shows that the high-accuracy PPM schemes can used to simulate fame and inert gas past a cylinder obstacle effectively. The numerical computation of the flame past the cylinder obstacle indicates that before the flame passes the cylinder obstacle, the gas expansion due to combustion causes the unburned gases in front of the flame to flow and to form the inert gas past the cylinder obstacle. This is similar to the inert gas past the cylinder obstacle without combustion. But there are obvious differences between the fame and inert gas past the cylinder obstacle when and after the flame passes the cylinder obstacle.