Extrapolated discontinuity tracking for complex 2D shock interactions. (English) Zbl 1507.76132
Summary: A new shock-tracking technique that avoids re-meshing the computational grid around the moving shock-front was recently proposed by the authors [J. Comput. Phys. 412, Article ID 109440, 24 p. (2020; Zbl 1436.76016)]. The method combines the unstructured shock-fitting [R. Paciorri and A. Bonfiglioli, in: Shock waves. 26th international symposium on shock waves. Vol. 2. Selected papers based on the presentations at the symposium, Göttingen, Germany, July 15–20, 2007. Berlin: Springer. 1035–1040 (2009; Zbl 1169.76415)] 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.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76L05 | Shock waves and blast waves in fluid mechanics |
Keywords:
shock-tracking; shock-fitting; unstructured grids; embedded boundary; shock interactions; Taylor expansionsSoftware:
GmshReferences:
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