Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD

Abstract

Linear Simulations of the Cylindrical Richtmyer-MeshkovInstability in Hydrodynamics and MHD Song GaoThe Richtmyer-Meshkov instability occurs when density-stratified interfaces are impulsively accelerated, typically by a shock wave. We present a numerical method to simulate the Richtmyer-Meshkov instability in cylindrical geometry. The ideal MHD equations are linearized about a time-dependent base state to yield linear partial differential equations governing the perturbed quantities. Convergence tests demonstrate that second order accuracy is achieved for smooth flows, and the order of accuracy is between first and second order for flows with discontinuities.Numerical results are presented for cases of interfaces with positive Atwood number and purely azimuthal perturbations. In hydrodynamics, the Richtmyer-Meshkov instability growth of perturbations is followed by a Rayleigh-Taylor growth phase.In MHD, numerical results indicate that the perturbations can be suppressed for sufficiently large perturbation wavenumbers and magnetic fields. 5 ACKNOWLEDGEMENTSSincere thanks to my supervisor, Prof. Ravi Samtaney, for his profound knowledge, patience and enthusiasm.Thanks to the members of my thesis examination committee, Prof. Sigurdur Thoroddsen and Prof.Georgiy Stenchikov, for their valuable comments and precious time.Thanks to Dr. Manuel Lombardini, for the interesting discussion and invaluable help. Thanks to Mr. Wei Gao, for his great encouragement.Thanks to my parents, for raising me up, and my unmet wife.Last but not least, special thanks to Dr. Fabrizio Bisetti, for the sharp lesson he has taught me. 6

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

“…In this paper, we have not presented detailed results on numerical convergence and order of accuracy of the proposed method. Numerical convergence tests of this method, performed by Gao, 24 show second order accuracy for smooth initial conditions. The method proposed here is very similar to that developed by Samtaney 18 for Cartesian slab geometry, which exhibits second order convergence for smooth flows and convergence rates between one and two for flows with shocks.…”