×

A method to simulate linear stability of impulsively accelerated density interfaces in ideal-MHD and gas dynamics. (English) Zbl 1173.76029

Summary: We present a numerical method to analyze the linear stability of impulsively accelerated density interfaces in two dimensions such as those arising in the Richtmyer-Meshkov instability. The method uses an Eulerian approach, and is based on an upwind method to compute the temporally evolving base state and a flux vector splitting method for the perturbations. The method is applicable to either gas dynamics or magnetohydrodynamics. Numerical examples are presented for cases in which a hydrodynamic shock interacts with a single or double density interface, and with a doubly shocked single density interface. Convergence tests show that the method is spatially second-order accurate for smooth flows, and between first- and second-order accurate for flows with shocks.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76E17 Interfacial stability and instability in hydrodynamic stability
76L05 Shock waves and blast waves in fluid mechanics
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76W05 Magnetohydrodynamics and electrohydrodynamics
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Richtmyer, R. D., Taylor instability in shock acceleration of compressible fluids, Commun. Pure Appl. Math., XIII, 297-319 (1960)
[2] Ye. Meshkov, Instability of a shock wave accelerated interface between two gases, NASA Tech. Trans., NASA TT F-13074, 1970.; Ye. Meshkov, Instability of a shock wave accelerated interface between two gases, NASA Tech. Trans., NASA TT F-13074, 1970.
[3] Yang, Y.; Zhang, Q.; Sharp, D. H., Small amplitude theory of Richtmyer-Meshkov instability, Phys. Fluids, 6, 5, 1856-1873 (1994) · Zbl 0831.76040
[4] Hawley, J. F.; Zabusky, N. J., Vortex paradigm for shock-accelerated density-stratified interfaces, Phys. Rev. Lett., 63, 1241-1244 (1989)
[5] Samtaney, R., Suppression of the Richtmyer-Meshkov instability in the presence of a magnetic field, Phys. Fluids, 15, 8, L53-L56 (2003) · Zbl 0592.60055
[6] Wheatley, V.; Pullin, D. I.; Samtaney, R., Stability of an impulsively accelerated density interface in magnetohydrodynamics, Phys. Rev. Lett, 95, 125002 (2005) · Zbl 1065.76207
[7] Wheatley, V.; Pullin, D. I.; Samtaney, R., Regular shock refraction at an oblique planar density interface in magnetohydrodynamics, J. Fluid Mech., 522, 179-214 (2005) · Zbl 1065.76207
[8] Jacobs, J. W.; Klein, D. L.; Jenkins, D. G.; Benjamin, R. F., Instability growth-patterns of a shock-accelerated thin fluid layer, Phys. Rev. Lett., 70, 5, 583-586 (1993)
[9] Prestridge, K.; Rightley, P. M.; Vorobieff, P.; Benjamin, R. F.; Kurnit, N. A., Simultaneous density-field visualization and PIV of a shock-accelerated gas curtain, Exp. Fluids, 29, 4, 339-346 (2000)
[10] Godlewski, E.; Raviart, P-A, The linearized stability of solutions of nonlinear hyperbolic systems of conservation laws A general numerical approach, Math. Comput. Simul., 50, 77-95 (1999) · Zbl 1027.65124
[11] Gardiner, T. A.; Stone, J. M., An unsplit Godunov method for ideal MHD via constrained transport, J. Comput. Phys., 205, 509-539 (2005) · Zbl 1087.76536
[12] Crockett, R. K.; Colella, P.; Fisher, R. T.; Klein, R. I.; McKee, C. F., An unsplit cell-centered Godunov method for ideal MHD, J. Comput. Phys., 203, 422-448 (2005) · Zbl 1143.76599
[13] Falle, S. A.E. G.; Komissarov, S. S.; Joarder, P., A multidimensional upwind scheme for magnetohydrodynamics, Mon. Not. R. Astron. Soc., 297, 1, 265-277 (1998)
[14] Powell, K. G.; Roe, P. L.; Linde, T. J.; Gombosi, T. I.; DeZeeuw, D. L., A solution-adaptive upwind scheme for ideal magnetohydrodynamics, J. Comput. Phys., 154, 284-300 (1999) · Zbl 0952.76045
[15] Hill, D. J.; Pantano, C.; Pullin, D. I., Large-eddy simulation and multiscale modelling of a Richtmyer-Meshkov instability with reshock, J. Fluid Mech., 557, 29-61 (2006) · Zbl 1094.76031
[16] Latini, M.; Schilling, O.; Don, W. S., Effects of WENO flux reconstruction order and spatial resolution on reshocked two-dimensional Richtmyer-Meshkov instability, J. Comput. Phys., 221, 805-836 (2007) · Zbl 1107.65338
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.