The rep rate of an inertial fusion energy facility depends on the time-dependent response of the chamber environment between target ignitions. The fusion burn following the target ignition releases large quantities of energy into the chamber. This energy should be removed and the environment should be returned to a quiescent state so that the new fusion target can be positioned for the next cycle. Understanding the hydrodynamic transport of this energy through the chamber fill gas is essential because the multidimensional geometry effects become important on the long time scale, as the fluid interacts with the vessel wall containing various beam access ports. This interaction affects several different modes of the chamber species transport, including convection induced by shock waves and secondary flow, molecular diffusion, electron conductivity and radiation. In order to investigate these phenomena, we have developed SPARTAN code as an assembly of algorithms that were the most suitable for an accurate treatment of the computational problem, such as shock wave resolution and tracking, underlying flow physics and complex wall geometry. This study demonstrates that the geometry effects are critical in affecting the flow during the first 50 milliseconds following the target ignition. Thermal diffusion by molecules and free electrons has only a moderate effect in reducing the temperature extrema and is not sufficient to cool down the chamber to the equilibrium with the chamber wall within 100 ms. Radiation of the background plasma was identified as the only transport mechanism that has approached to this goal, making the chamber environment more suitable for inserting the next target.