A front-tracking/ghost-fluid method for the numerical simulations of Richtmyer–Meshkov Instability

We present an increasingly accurate and robust front-tracking (FT) method coupled with the ghost-fluid method (GFM) for the numerical simulations of shock-induced turbulent mixing. The FT-GFM method with the higher-order weighted essentially non-oscillatory (WENO) schemes is used to study the evolution of the complex and moving fluid interfaces in compressible flows. We demonstrate the improvements in the late-time dynamics of the fluid interfaces and the effect of the high-order WENO schemes with monotonicity preserving bounds on several test problems. One-dimensional scalar advection, Sod’s shock tube, shock-entropy wave interaction problems, and two-dimensional shock tube Richtmyer–Meshkov instability (RMI) between air and SF 6 simulations are performed in order to show the improvements achieved using the new method. The fifth- and ninth-order WENO schemes with and without monotonicity preserving bounds are explored in the numerical solution of the shock-driven interface problem. • The front-tracking/ghost-fluid method (FT/GFM) with monotonicity preserving ninth-order weighted essentially non-oscillatory (MPWENO9) scheme improves Richtmyer–Meshkov instability simulations. • RMI simulations presented here show a very good agreement with the single-mode shock tube experiments of Collins and Jacobs 2002 for the incident shock strength M = 1 . 21 . • The spike roll-up structures in experiments are captured with MPWENO9 fine grid FT/GFM simulations.