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Extrapolated DIscontinuity Tracking for complex 2D shock interactions

Mirco Ciallella, Mario Ricchiuto, Renato Paciorri, Aldo Bonfiglioli

TL;DR

Further algorithmic improvements are described which make the extrapolated Discontinuity Tracking Technique (eDIT) capable of dealing with complex shock-topologies featuring shock-shock and shock-wall interactions.

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.

Extrapolated DIscontinuity Tracking for complex 2D shock interactions

TL;DR

Further algorithmic improvements are described which make the extrapolated Discontinuity Tracking Technique (eDIT) capable of dealing with complex shock-topologies featuring shock-shock and shock-wall interactions.

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.

Paper Structure

This paper contains 24 sections, 33 equations, 29 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Generalities
  3. Extrapolated DIscontinuity Tracking ($eDIT$)
  4. Generalities
  5. Geometrical setting
  6. Definition of the sub-domains
  7. Solution update using the CFD solver
  8. Surrogate discontinuity conditions update
  9. Computational mesh to discontinuity mesh transfer
  10. Riemann variables and jump conditions enforcement
  11. Discontinuity mesh to computational mesh transfer
  12. Front displacement and nodal re-initialization
  13. Evaluation of the nodal gradients
  14. Remarks on conservation
  15. Numerical Results
  16. ...and 9 more sections

Figures (29)

  • Figure 1: The computational-mesh is obtained by removing those cells of the background mesh that are crossed by the front-mesh.
  • Figure 2: Definition of surrogate boundaries when multiple fronts interact; in the regular reflection shown here, the surrogate boundaries marked in green are located upstream w.r.t. the incident and reflected shocks, whereas those marked in red are located downstream.
  • Figure 3: The solution update is performed using the computational mesh.
  • Figure 4: First transfer between the the surrogate boundaries and the front-mesh.
  • Figure 5: The front overtakes a grid-point of the background mesh during its motion.
  • ...and 24 more figures