In the present study, behavior of thermo-chemical fluid in a combustion chamber of engine was numerically analyzed using the finite difference method with Navier-Stokes equations including chemical reactions. As the position of a piston changes with the lapse of time, grid points composing a computational mesh are not always on the piston head. Therefore, values of conserved quantities on the piston head were found by series expansion from near grid points and were utilized in the calculation. Aiming at capturing the feature of premixed compression ignition, a stoichiometric gas mixture of hydrogen and air was used with a detailed reaction mechanism. Numerical method executed in the present case is the semi-implicit MacCormack-TVD scheme with the second order accuracy. It was found from the calculated results that a new computation approach to the premixed compression ignition could obtain valid solutions for us without grid regeneration.