A Self-Similar Diffuse Interface Method for a Rotating Ablating Cylinder

A melting, sublimating, ablating, or deflagrating solid exerts a variety of boundary conditions on the fluid as mass, momentum, angular momentum, and energy are exchanged between the phases. By treating the interface implicitly, Diffuse Interface Methods (DIMs) do not require complex interface tracking or reconstruction; when coupled with adaptive mesh refinement (AMR), which allows sufficient resolution of the interface at minimal computational cost, a diffuse interface approach provides a straightforward framework for modeling multi-phase problems on a single mesh. The introduction of artificial diffusivity naturally comes with the introduction of an artificial numerical length scale. The authors present a robust DIM which preserves self-similarity for phase boundaries between a solid and viscous, compressible flow - that is, a DIM in which the diffuse length scale has no adverse effects. We consider a rotating, sublimating solid cylinder in viscous compressible flow with mass and energy flux across the evolving phase boundary; stability of this method is considered, along with convergence analysis to the equivalent free-boundary problem. A variety of analytic solutions for cylinders in viscous compressible flow are included for verification.