Adaptive characteristics-based matching for compressible multifluid dynamics

This paper presents an evolutionary step in sharp capturing of shocked, high acoustic impedance mismatch (AIM) interfaces in an adaptive mesh refinement (AMR) environment. The central theme which guides the present development addresses the need to optimize between the algorithmic complexities in advanced front capturing and front tracking methods developed recently for high AIM interfaces with the simplicity requirements imposed by the AMR multi-level dynamic solutions implementation. The paper shows that we have achieved this objective by means of relaxing the strict conservative treatment of AMR prolongation/restriction operators in the interfacial region and by using a natural-neighbor-interpolation (NNI) algorithm to eliminate the need for ghost cell extrapolation into the other fluid in a characteristics-based matching (CBM) scheme. The later is based on a two-fluid Riemann solver, which brings the accuracy and robustness of front-tracking approach into the fast local level set front-capturing implementation of the CBM method. A broad set of test problems (including shocked multi-gaseous media, bubble collapse, underwater explosion and shock passing over a liquid drop suspended in a gaseous medium) was performed and the results demonstrate that the fundamental assumptions/approximations made in modifying the AMR prolongation/restriction operators and in using the NNI algorithm for interfacial treatment are acceptable from the accuracy point of view, while they enable an effective implementation and utility of the structured AMR technology for solving complex multiphase problems in a highly compressible setting.