Abstract:The Unified Gas Kinetic Scheme (UGKS) was developed by Xu Kun especially for simulating rarefied flows. In UGKS, the conservation constraint can not be satisfied with conventional Discrete Ordinate Method (DOM) and numerical error would be introduced. We found theoretically and numerical experimentally that the error was proportional to the freestream Mach number and inversely proportional to the freestream Knudsen number. Conservative discrete ordinate method (CDOM) was introduced with which the conservation constraint was satisfied at discrete level. The supersonic and hypersonic flows around a cylinder at different Knudsen numbers were simulated and results showed that whether the conservative constraint was satisfied would have a big effect on the variable distributions and the drag coefficients when the Mach number was high or the Knudsen number was low. With CDOM, the grid-free solution could be obtained with a relative coarse velocity grid, resulting in a maximum cost reduction of 2/3.