A new shock-tracking technique that avoids re-meshing the computational grid around the moving shock-front was recently proposed by the authors (Ciallella et al., 2020). The method combines the unstructured shock-fitting (Paciorri and Bonfiglioli,2009) approach, developed in the last decade by some of the authors, with ideas coming from embedded boundary methods. In particular, second-order extrapolations based on Taylor series expansions are employed to transfer the solution and retain high order of accuracy. This paper describes the basic idea behind the new method and further algorithmic improvements which make the extrapolated Discontinuity Tracking Technique (eDIT) capable of dealing with complex shock-topologies featuring shock-shock and shock-wall interactions occurring in steady problems. This method paves the way to a new class of shock-tracking techniques truly independent on the mesh structure and flow solver. Various test-cases are included to prove the potential of the method, demonstrate the key features of the methodology, and thoroughly evaluate several technical aspects related to the extrapolation from/onto the shock, and their impact on accuracy, and conservation.

翻译：近期，作者们提出了一种新的激波追踪技术(Ciallella等，2020)，该技术避免了围绕移动激波前沿对计算网格进行重新剖分。该方法将作者团队过去十年发展的非结构化激波拟合方法(Paciorri和Bonfiglioli，2009)与嵌入边界方法的思想相结合。具体而言，采用基于泰勒级数展开的二阶外推来传递解并保持高阶精度。本文阐述了该新方法的基本思想及进一步的算法改进，使外推间断追踪技术(eDIT)能够处理包含激波-激波和激波-壁面相互作用的复杂稳态问题激波拓扑结构。该方法为发展真正独立于网格结构和流场求解器的新型激波追踪技术开辟了道路。文中包含多种算例以验证该方法潜力，展示其关键特性，并深入评估了与激波外推/内插相关的若干技术细节及其对精度和守恒性的影响。