During its initial re-entry, the primary issues are heating related. Thermodynamic testing is critical to make sure that the Space Shuttle survives the incredible heat. During the next phase the Space Shuttle is a very high-speed glider. Mach numbers is important during this phase. The space shuttle does have to slow down to land, and during this phase testing at the correct Mach and Reynolds numbers together becomes important.
Digital computations are still extremely difficult to model accurately.
Tunnels are very important to validate computational models in all flight regimes, especially low speed flight. If anyone has driven along hwy 101 through Mountain View, CA you probably have seen a very large strange looking structure over at Moffett Field. The structure I am referring to looks like a huge flat wall with a bell shaped curve behind it. This is the inlet for the works largest wind tunnel. We use this wind tunnel to test real aircraft.