How distinct is fluid dynamics from continuum physics? I've heard it is a subset and by the definition of the subject's name, it seems likely to be the case. Can anyone please clarify?
Continuum physics, or more specifically continuum mechanics is paradigm that seeks to describe the bulk properties of a system by treating it as a continuum. This can include fluids and bulk deformation and vibrations in solids. One could argue that the liquid drop model of the nucleus was an example of continuum physics. From a fundamental perspective, before we understood the structure of the atom, continuum mechanics could have been seen as "fundamental" in the sense that the continuum equations defined the irreducible characteristics of a system. We even has the pudding+raisin model of matter before the Rutherford scattering experiment illuminated the internal structure of matter. Now we still use continuum models as a modeling, or computational, and theoretical tool for describing bulk properties of matter. A continuum model can be developed from first principles using a discrete N-body system and taking the limit as N-->infinity while other properties go to zero. Or it can be hypothesized to have certain properties based on observational evidence. A good book on continuum methods is Classical Field Theory by Davison Soper.