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How does a computational astrophysicist get the most out of their code? For some, the goal is to make simulations that mimic reality as closely as possible. However, in this talk I argue for a "computational experiment" approach, where the end goal is not to reproduce the system realistically, but to understand the fundamental laws governing it. I will make the case that this approach often leads to a much more clear understanding of the underlying physical system. First, I will describe some of the specialized numerical codes I have developed, which employ unique moving meshes tailored to the physical system being studied. Next, I will discuss a few important examples to which I have applied my codes and "computational experiment" approach; one example involving gap opening in protoplanetary disks, and another investigating the neutron star merger event GW170817.