Adaptive Characteristics-Based Matching (aCBM): a Method for Interfacial Dynamics in Compressible Multiphase Flows

This work is motivated by the need for a high-fidelity numerical treatment of compressible flows with multimaterial interfaces. Of particular interest are immiscible flows with high Acoustic Impedance Mismatch (AIM) interfaces, such as those between gases and liquids, under both weak and strong shock wave conditions. These types of flow are encountered in numerous generically-important processes, such as propagation of shock waves in bubbly media, and interfacial instability and mixing, as well as in applications, such as explosive dispersal of liquids or solids, and atmospheric dissemination of liquid chemical agents [18]. Here, we capitalize on recent progress made by front capturing ([15],[16] and [7]) and front tracking ([5] and [6]) methods to deploy an adaptive mesh refinement strategy such as needed to cope with the often multiscale nature of such flows in practical settings.