Extrapolated DIscontinuity Tracking for complex 2D shock interactions

TL;DR

This paper introduces an advanced shock-tracking method that accurately handles complex 2D shock interactions without re-meshing, combining unstructured shock-fitting and embedded boundary ideas for high-order precision.

Contribution

The paper presents the extrapolated Discontinuity Tracking Technique (eDIT), a novel mesh-independent shock-tracking approach capable of managing complex shock-topologies with improved accuracy and robustness.

Findings

Successfully handles shock-shock and shock-wall interactions.

Maintains high-order accuracy through Taylor series extrapolations.

Demonstrates robustness and effectiveness across various test cases.

Abstract

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.