Self-similar diffuse boundary method for phase boundary driven flow

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