Keywords: scheme with customizable dissipative properties, gas flow calculation, instability evolution, interface
References
1. Cocchi J.P., Saurel R., Loraud J.C. Treatment of interface problems with Godunov-type schemes. Shock Waves, 1996, vol. 5, no. 6, pp. 347–357. doi: 10.1007/pl00003878
2. Toro E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics. Berlin, Springer-Verlag, 2009, 724 p.
3. Jiang G.-S., Shu C.-W. Efficient implementation of weighted ENO schemes. Journal of Computational Physics, 1996, vol. 126, pp. 202–228. doi: 10.1006/jcph.1996.0130
4. Shi J., Zhang Y.-T., Shu C.-W. Resolution of high order WENO schemes for complicated flow structures Journal of Computational Physics, 2003, vol. 186, no. 2, pp. 690–696. doi: 10.1016/S0021-9991(03)00094-9
5. Coralic V., Colonius T. Finite-volume WENO scheme for viscous compressible multicomponent flows. Journal of Computational Physics, 2014, vol. 274, pp. 95–121. doi: 10.1016/j.jcp.2014.06.003
6. Bulat M.P., Volobuev I.A., Volkov K.N., Pronin V.A. Numerical simulation of regular and Mach reflection of shock wave from the wall. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2017, vol. 17, no. 5, pp. 920–928. (In Russian) doi: 10.17586/2226-1494-2017-17-5-920-928
7. Tolstykh A.I. On families of compact fourth- and fifth-order approximations involving the inversion of two-point operators for equations with convective terms. Computational Mathematics and Mathematical Physics, 2010, vol. 50, no. 5, pp. 848–861. doi: 10.1134/S096554251005009X
8. Shen Y.-Q., Zha G.-C. Generalized finite compact difference scheme for shock/complex flow field interaction. Journal of Computational Physics, 2011, vol. 230, no. 12, pp. 4419–4436. doi: 10.1016/j.jcp.2011.01.039
9. Mikhailovskaya M.N., Rogov B.V. Monotone compact running schemes for systems of hyperbolic equations. Computational Mathematics and Mathematical Physics, 2012, vol. 52, no. 4, pp. 578–600. doi: 10.1134/S0965542512040124
10. Christensen R.B. Godunov Methods on a Staggered Mesh - An Improved Artificial Viscosity. Technical Report UCRL-JC-105269, 1990, 11 p.
11. Shankar S.K., Kawai S., Lele S. Numerical simulation of multicomponent shock accelerated flows and mixing using localized artificial diffusivity method. Proc. 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Orlando, USA, 2010, art. 2010-0352.
12. Kurganov A., Liu Y. New adaptive artificial viscosity method for hyperbolic systems of conservation laws. Journal of Computational Physic, 2012, vol. 231, no. 24, pp. 8114–8132. doi: 10.1016/j.jcp.2012.07.040
13. Tagirova I. Yu., Rodionov A. V. Application of the artificial viscosity for suppressing the carbuncle phenomenon in Godunov-type schemes. Mathematical Models and Computer Simulations, 2016, vol. 8, no. 3, pp. 249–262. doi: 10.1134/S2070048216030091
14. Sadin D.V. TVD scheme for stiff problems of wave dynamics of heterogeneous media of nonhyperbolic nonconservative type. Computational Mathematics and Mathematical Physics, 2016, vol. 56, no. 12, pp. 2068–2078. doi: 10.1134/S0965542516120137
15. Sadin D.V. Schemes with customizable dissipative properties as applied to gas-suspensions flow simulation. Mathematical Models and Computer Simulations, 2017.
16. Wong M.L., Lele S.K. High-order localized dissipation weighted compact nonlinear scheme for shock- and interface-capturing in compressible flows. Journal of Computational Physics, 2017, vol. 339, no. 15, pp. 179–209. doi: 10.1016/j.jcp.2017.03.008.
17. Liska R., Wendroff B. Comparison of several difference schemes on 1D and 2D test problems for the Euler equations. SIAM Journal on Scientific Computing, vol. 25, no. 3, pp. 995–1017. doi: 10.1137/S1064827502402120
18. Gottlieb S., Shu C.-W. Total variation diminishing Runge-Kutta schemes. Mathematics of Computation, 1998, vol. 67, no. 221, pp. 73–85. doi: 10.1090/S0025-5718-98-00913-2
19. Jiang G.-S., Tadmor E. Nonoscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM Journal on Scientific Computing, 1998, vol. 19, no. 6, pp. 1892–1917. doi: 10.1137/S106482759631041X
20. Colella P., Woodward P. The piecewise parabolic method (PPM) for gas-dynamical simulations. Journal of Computational Physics, 1984, vol. 54, no. 1, pp. 174–201. doi: 10.1016/0021-9991(84)90143-8
21. Woodward P., Colella P. The numerical simulation of
two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 1984, vol. 54, no. 1, pp. 115–173. doi: 10.1016/0021-9991(84)90142-6