There's no reason to believe our universe is uncomputable. It may require vast resources, in excess of what our universe possesses (by definition, in some sense), but we have no ability to say that there can exist no other possible universe that may not only possess these resources, but consider our entire universe the moral equivalent of a homework problem running on a toy computer.
Even if our universe is in some sense based on real numbers (in the math sense), there's no apparent reason to believe that arbitrarily accurate simulations couldn't be run of it. (Or, alternatively, our host universe may also have real numbers and be able to use them for simulation purposes.)
Even if our universe is in some sense based on real numbers (in the math sense), there's no apparent reason to believe that arbitrarily accurate simulations couldn't be run of it. (Or, alternatively, our host universe may also have real numbers and be able to use them for simulation purposes.)