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.

近年来，人们对高阶不连续方案的研究兴趣日益浓厚。随着理论基础和框架的建立，最近人们付出了更多的努力来实现复杂多物理流建模的不连续方案能力。在利用高阶不连续方案的兼容数值方法和算法的开发方面已经取得了实质性的成就和里程碑。本研究的目的是全面调查和总结与不连续方案相关的关键算法组件，同时确定其多相流和多组分流建模能力的当前技术水平。此外，本综述研究了最近文献中的代表性应用，以展示不连续方案在各种场景中的有希望的性能。该评论还确定了先前研究工作中遇到的局限性和瓶颈，并为未来的研究提供了建议。本综述的主要目的是为该领域的研究人员提供有价值的指南，促进基于不连续方案的新计算流体动力学 (CFD) 功能的开发。