Is it a subfield of theory? What about - uhmm - “numerical experiments” (if there’s something like that)?
One could consider numerical simulation a third paradigm of science besides theory and experiment (see e.g. this link).
The term “numerical experiment”, however, would suggest a black box concept, i.e. you feed some input into the code and get numbers out, but don’t necessarily understand how and why it works and therefore not even if the output means anything.
So I would prefer the term “simulation” and make computational physics a part of theory and apply it to problems which are too complex to be solved by hand. Along this line scientific computing can aim at providing new “tools of discovery” of complex phenomena.
What do you think “scientific computing” is about and do you think it is important at all to decide which field it belongs to?