Shock Waves

pp 1–13 | Cite as

An adaptive discontinuity fitting technique on unstructured dynamic grids

  • S. Chang
  • X. Bai
  • D. Zou
  • Z. Chen
  • J. LiuEmail author
Original Article


A novel, adaptive discontinuity fitting technique has been further developed on unstructured dynamic grids to fit both shock waves and contact discontinuities in steady flows. Moreover, in order to efficiently obtain shock-fitting solutions, two strategies, direct-fitting and indirect-fitting, have been proposed to, respectively, deal with simple and complex flows. More specifically, without first computing the flow field by a shock-capturing method, the direct-fitting strategy, mainly dealing with these discontinuities of which topologies are clearly known, can quickly obtain the solutions by initially presetting an approximate discontinuity front. By contrast, the indirect-fitting strategy, especially in coping with the complicated discontinuity structures, must utilize both shock-capturing solutions and shock detection techniques to first determine initial discontinuity locations. The two strategies have been successfully applied to a series of compressible flows, including a two-dimensional flow with type IV shock–shock interaction and a three-dimensional flow with type VI interaction. In addition, comparing the fully-fitting solution with the partially-fitting solution in the discontinuity interaction region, it is indicated that an accurate result can be acquired if all the discontinuities in the vicinity of interaction points are fully fitted. Nevertheless, the computational accuracy of expansion waves can indeed significantly affect the downstream discontinuities.


Shock fitting Unstructured dynamic grids Supersonic flow Shock interactions 



This work has been financially supported by the National Natural Science Foundation of China (Grant No. 11872144). Moreover, Fan Zhang at the School of Aeronautics and Astronautics, Sun Yat-sen University, is appreciated for offering advice on improving this article.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina
  2. 2.School of Aeronautics and AstronauticsDalian University of TechnologyDalianChina
  3. 3.China Aerodynamics Research and Development CenterMianyangChina

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