We have simulated the flow in a real cordierite DPF using the lattice Boltzmann method. Inner structure of the filter is analyzed by a 3D X-ray CT technique. Two processes of soot deposition for PM trap and soot combustion for filter regeneration process are considered. Especially, the effect of NO2 on the soot oxidation is examined, which is recently proposed as on-board regeneration system. The reaction rate has been determined based on previous experimental data. The estimated values of Arrhenius factor and activation energy are A = 146 1/s, E = 79.5 kJ/mol with NO2, and A = 1.20 1/s, E = 64.9 kJ/mol without NO2. Results show that, the flow field and pressure change inside the filter are clearly visualized. The pressure distribution depends on the non-uniformity of pore structure. The flow is largely changed with soot deposition, with higher pressure drop across the filter (filter back-pressure). The obtained correlation between total accumulated soot and the filter back-pressure is well in accordance with reported experimental results. In combustion simulation, the effect of NO2 addition to promote the soot oxidation is confirmed. These are useful information to develop the future regenerating DPF system.