Shock Waves

, Volume 29, Issue 1, pp 101–115 | Cite as

Dynamics of shock wave diffraction over sharp splitter geometry using entropy-based artificial viscosity method

  • A. ChaudhuriEmail author
  • G. B. Jacobs
Original Article


This paper reports the numerical analysis of shock wave diffraction over a convex sharp splitter geometry, focusing on the mechanism of the shock diffraction and the longtime behavior of shock–vortex dynamics. The flow evolution with shock–vortex dynamics for incident shock Mach number, \({M}_{{\mathrm {s}}} = 1.59\), is found to be in excellent agreement with the previous experimental results. We use a recent entropy-generation-based artificial viscosity (AV) method in conjunction with a high-order explicit discontinuous spectral element method (DSEM) to resolve these complex interactions. The AV is coupled with a shock sensor switch to attain optimal dissipations. Simulations capture the essential wave diffraction, transverse wave interaction with the deforming and growing primary vortex, and weaker secondary vortices arising from the Kelvin–Helmholtz instability. A quantification of the artificial dissipation of the numerical scheme is made by comparing the components of the kinetic energy dissipation rate and the pressure dilatation term. A new detailed transient flow analysis is also presented to address the shock dynamics, shock–vortex interaction, and the evolution of the flow topology with the probability density functions of various parameters of the enstrophy transport equation and the invariants of the velocity gradient tensor. The analysis reveals the mechanism of unwinding of vortices and its link with the divergence of the Lamb vector. A positive correlation is found between enstrophy and the imaginary part of the eigenvalues. Real parts of the two eigenvalues are associated with high dilatation shock regions and the outer edges of the vortices, respectively.


Shock diffraction High-order numerical scheme Shock–vortex interaction Artificial viscosity 



This work used the resources of Extreme Science and Engineering Discovery Environment (XSEDE) [27] supported by National Science Foundation of USA, Grant No. ACI-1053575. The authors greatly acknowledge the collaboration with W. S. Don of Ocean University of China and F. Mashayek of University of Illinois at Chicago.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Civil Engineering and Energy TechnologyHiOA (Oslo And Akershus University College of Applied Sciences)OsloNorway
  2. 2.Department of Aerospace Engineering and Engineering MechanicsSan Diego State UniversitySan DiegoUSA

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