Fully-implicit interface tracking for all-speed multifluid flows

A new interface tracking method for all-speed multi-fluid flows is introduced. The key feature of the method is that the interface motion and fluid dynamics are fully-(non-linearly)-coupled, which allows to completely eliminate operator-splitting temporal errors. The direct benefits of this treatment are a) the method is L-stable, permitting time steps controlled only by accuracy requirements; b) the method is high-order-accurate in time; c) the method is fully-conservative, even at the interface, and robust (no pressure-velocity oscillations, in difference to previous attempts for conservative interface tracking). The keys to these advantages are the high-order sharp cut-cell-based interface treatment combined with implicit Runge-Kutta (ESDIRK) scheme within the physics-based-preconditioned Jacobian-free Newton-Krylov method (JFNK) [KK03]. Interfaces are tracked by hybridizing the Lagrangian Marker tracking with the Eulerian JFNK-based Re-Distancing/Level-Set algorithm (MRD/LS) [NKMK08]; all non-linearly coupled with the JFNK-based "recovery Discontinuous Galerkin" (rDG-JFNK) for all-speed fluid flows [NTPMK08, PNMK08].