  Interactions between an evolving solid and inviscid flow can result in
substantial computational complexity, particularly in circumstances involving
varied boundary conditions between the solid and fluid phases. Examples of such
interactions include melting, sublimation, and deflagration, all of which
exhibit bidirectional coupling, mass/heat transfer, and topological change of
the solid-fluid interface. The diffuse interface method is a powerful technique
that has been used to describe a wide range of solid-phase interface-driven
phenomena. The implicit treatment of the interface eliminates the need for
cumbersome interface tracking, and advances in adaptive mesh refinement have
provided a way to sufficiently resolve diffuse interfaces without excessive
computational cost. However, the general scale-invariant coupling of these
techniques to flow solvers has been relatively unexplored. In this work, a
robust method is presented for treating diffuse solid-fluid interfaces with
arbitrary boundary conditions. Source terms defined over the diffuse region
mimic boundary conditions at the solid-fluid interface, and it is demonstrated
that the diffuse length scale has no adverse effects. To show the efficacy of
the method, a one-dimensional implementation is introduced and tested for three
types of boundaries: mass flux through the boundary, a moving boundary, and
passive interaction of the boundary with an incident acoustic wave. These
demonstrate expected behavior in all cases. Convergence analysis is also
performed and compared against the sharp-interface solution, and linear
convergence is observed. This method lays the groundwork for the extension to
viscous flow, and the solution of problems involving time-varying mass-flux
boundaries.
