Direct numerical simulations are tried using finite difference methods to investigate the starting processes of the ram accelerator in Hiroshima University, the ram acceleration tube of which has a rectangular bore for easy observation. A projectile and an igniter fly at speed below C-J velocity from an evacuated chamber into a ram acceleration tube, where hydrogen-oxygen-nitrogen gas mixtures are filled as combustible gases. When the acceleration tube is filled by carbon dioxide as a non-reactive gas for the first test, the results of the numerical solutions give a good agreement with the experimental results. When combustible gas mixtures are filled in the acceleration tube, we could not get a solution without detonation or quenching. This kind of difficulty to start is also found in the experiments. The numerical results show how the igniter works in the starting process, those help our experiments.