Recent progress on high-order discontinuous schemes for simulations of multiphase and multicomponent flows

There have been growing research interests in high-order discontinuous schemes over recent years. With established theoretical basis and framework, more efforts have recently been taken to enable discontinuous-scheme capabilities for modeling complex multi-physical flows. Substantial achievements and milestones have been reached in the development of compatible numerical methods and algorithms that leverage high-order discontinuous schemes. The objective of this study is to comprehensively survey and summarize the key algorithmic components relevant to discontinuous schemes, while identifying the current state of the art in their capabilities for modeling multiphase and multicomponent flows. Furthermore, this review examines representative applications from recent literature to showcase the promising performance of discontinuous schemes in various scenarios. The review also identifies the limitations and bottlenecks encountered in previous research efforts and offers recommendations for future investigations. The primary aim of this review is to serve as a valuable guidebook for researchers in the field, facilitating the development of new computational fluid dynamics (CFD) capabilities based on discontinuous schemes.