Axisymmetric numerical simulations of the operation of the laser-driven in-tube accelerator have been carried out to investigate the dependencies of the propulsion performance on various conditions. The computational code covers from the generation of the blast wave to its interactions with the projectile and the acceleration wall. The thrust history and the momentum coupling coefficient evaluated from the numerical simulation depend on the fill pressure of the propellant gas and the projectile shape. The confinement effect using the projectile attached with a shroud attributes to high momentum coupling coefficient. The higher momentum coupling coefficient is also found for the lower fill pressure with the LITA50 configuration.