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.