When a shock wave interacts with a contact discontinuity, there may appear a reflected rarefaction wave, a deflected contact discontinuity and a refracted supersonic shock. The numerical simulation of shock wave refraction at a plane contact discontinuity separating gases with different densities is performed. Euler equations describing inviscid compressible flow were discretized using the finite volume method on unstructured meshes and WENO schemes. Time integration was performed using a third-order Runge–Kutta method. The wave structure resulting from regular shock refraction is determined allowing its properties to be explored. In order to visualize and interpret the results of numerical calculations, a procedure for identifying and classifying gas-dynamic discontinuities was applied. The procedure employed dynamic consistency conditions and digital image processing methods to determine flow structure and its quantitative characteristics. The results of the numerical and experimental visualizations were compared (shadow patterns, schlieren images, interferograms). The results computed are in an agreement with the theoretical and experimental predictions of a regular refraction of a shock wave on an inclined contact discontinuity.

Abd-El-Fattah, A.M. & Henderson, L.F. (1978). Shock waves at a fast-slow gas interface. Journal of Fluid Mechanics, 86, 15–32.

Banuti, D.T., Grabe, M. & Hannemann, K. (2011). Steady shock refraction in hypersonic ramp flow. AIAA Paper, 2011-2215.

Brouillette, M. (2002). The Richtmyer–Meshkov instability. Annual Review of Fluid Mechanicsm 34, 445–468.

Bulat, P.V. & Uskov, V.N. (2014). Shock and detonation wave in terms of view of the theory of interaction gasdynamic discontinuities. Life Science Journal, 11(8), 307–310.

Bulat, P.V. & Volkov, K.N. (2015a). Simulation of supersonic flow in a channel with a step on nonstructured meshes with the use of the WENO scheme. Journal of Engineering Physics and Thermophysics, 88(4), 848–855.

Bulat, P.V. & Volkov, K.N. (2015b). Using WENO schemes for simulation of reflected shock wave with a boundary level. Journal of Engineering Physics and Thermophysics, 88(5), 1163–1170.

Burago, N.G. & Kukudzhanov, V.N. (2005). A review of contact algorithms. The Institute for Problems in Mechanics of RAS, 1, 45–87.

Delmont, P., Keppens, R. & van der Holst, B. (2009). An exact Riemann solver based solution for regular shock refraction. Journal of Fluid Mechanics, 627, 33–53.

Dutta, S., Glimm, J., Grove, J.W., Sharp, D.H. & Zhang, Y. (2004). Error comparison in tracked and untracked spherical simulations. Computers and Mathematics with Applications, 48(10-11), 1733–1747.

Fang, B., Wang, Y.G. & Yuan, H. (2011). Reflection and refraction of shocks on an interface with a reflected rarefaction wave. Journal of Mathematical Physics, 52, 073702.

Henderson, L.F. (1989). On the refraction of shock waves. Journal of Fluid Mechanics, 198, 365–386 (1989).

Henderson, L.F., Colella, P. & Puckett, E.G. (1991). On the refraction of shock waves at a slow-fast gas interface. Journal of Fluid Mechanics, 224, 1–27.

Jahn, R.G. (1956). The refraction of shock waves at a gaseous interface, Journal of Fluid Mechanics, 1, 457–489.

Liu, T.C., Khoo, B.C. & Yeo, K.S. (2001). The simulation of compressible multi-medium flow. I. A new methodology with test applications to 1D gas–gas and gas–water cases. Computers and Fluids, 30(3), 291–314.

Nouragliev, R.R., Sushchikh, S.Y., Dinh, T.N. & Theofanous, T.G. (2005). Shock wave refraction patterns at interfaces. International Journal of Multiphase Flow, 31(9), 969–995.

Osher, S.J. & Fedkiw, R.P. (2003). Level set method and dynamic implicit surfaces, New York: Springer, 352 p.

Pember, R.B. & Anderson, R.W. (2001). Comparison of direct Eulerian Godunov and Lagrange plus remap, artificial viscosity schemes. AIAA Paper 2001-2644, 255-267.

Samtaney, R. (2003). Suppression of the Richtmyer–Meshkov instability in the presence of a magnetic field. Physics of Fluids, 15, 53–56.

Samtaney, R. & Meiron, D.I. (1997). Hypervelocity Richtmyer–Meshkov instability. Physics of Fluids, 9(6), 1783–1803.

Samtaney, R. & Pullin, D.I. (1996). On initial-value and self-similar solutions of the compressible Euler equations. Physics of Fluids, 8(10), 2650–2655.

Samtaney, R. & Zabusky, N.J. (1993). On shock polar analysis and analytical expressions for vorticity deposition in shock-accelerated density stratified interfaces. Physics of Fluids, 5(6), 285–1287.

Samtaney, R. & Zabusky, N. (2000). Visualization, extraction and quantification of discontinuities in compressible flows. Techniques and Examples, 317-344.

Schalkoff, R.J. (1988). Digital image processing and computer vision. New York: John Wiley & Sons, 377 p.

Uskov, V.N., Bulat, P.V. & Arkhipova L.P. (2014a) Gas-dynamic discontinuity conception. Research Journal of Applied Sciences, Engineering and Technology, 8(22), 2255–2259 (2014).

Uskov, V.N., Bulat, P.V. & Arkhipova, L.P. (2014b) Classification of gas-dynamic discontinuities and their interference problems,” Research Journal of Applied Sciences, Engineering and Technology, 8(22), 2248–2254.

Volkov, K.N. (2008). Unstructured-grid finite-volume discretization of the Navier-Stokes equations based on high-resolution difference schemes. Computational Mathematics and Mathematical Physics, 48(7), 1181-1202.

Vorozhtsov, E.V. (1990). On the classification of discontinuities by the pattern recognition methods. Computers and Fluids, 18(1), 35-74.

Wheatley, V., Pullin, D.I. & Samtaney, R. (2005). Regular shock refraction at an oblique planar density interface in magnetohydrodynamics, Journal of Fluid Mechanics, 522, 179–214.

Yang, X., Chern, I., Zabusky, N.J., Samtaney, R. & Hawley, J.F. (1992). Vorticity generation and evolution in shock-accelerated density-stratified interfaces. Physics of Fluids, 4(7), 1531–1540.

Zeng, S. & Takayama, K. (1996). On the refraction of shock wave over a slow-fast gas interface. Acta Astronautica, 38(11), 829–838.

Znamenskaya, I.A., Ivanov, I.E., Koroteyeva, E.Yu. & Orlov, D.M. (2011). Gas-dynamic phenomena during shock wave interaction with the cooling plasma of impulse surface discharge. Reports of the Russian Academy of Sciences, 439(5), 609–612.