[quote]I am interested in standing longitudinal wave and I would like to model numerically what happens (pressure temperature and velocity) inside a one-end closed tube.

Sound wave is a pressure wave. Please write down in more detail:
1. temperature: do you mean temperature of the air? Temperature is a global quantity (average of kinetic energy of gas).
what do you mean by you want to model it numerically?
2. What is the velocity you are talking about? wave velocity? ...?