Anti-diffusion interface sharpening technique for two-phase compressible flow simulations

In this paper we propose an interface sharpening technique for two-phase compressible-flow simulations based on volume-of-fluid methods. The idea of sharpening the two-fluid interface is to provide a correction algorithm which can be applied as post-processing to the volume-fraction field after each time step. For this purpose an anti-diffusion equation, i.e. a diffusion equation with a positive diffusion coefficient, is solved to counter-act the numerical diffusion resulting from the underlying VOF discretization. The numerical stability and volume-fraction boundedness in solving the anti-diffusion equation are ensured by a specified discretization scheme. No interface reconstruction and interface normal calculation are required in this method. All flow variables are updated with the sharpened volume-fraction field for ensuring the consistency of the variables, and the update of the phase mass, momentum and energy is conservative. Numerical results for shock-tube and shock-bubble interactions based on the ideal-gas EOS and shock contact problems based on the Mie–Grüneisen EOS show an improved interface resolution. The large-scale interface structures are in good agreement with reference results, and finer small-scale interface structures are recovered in a consistent manner as the grid resolution increases. As compared with reference high grid-resolution numerical results based on AMR algorithms, the interface roll-up phenomena due to the Richtmyer–Meshkov instability and the Kelvin–Helmholtz instability are recovered reliably for shock-bubble interactions involving different ideal gases.