A robust front tracking method: Verification and application to simulation of the primary breakup of a liquid jet

This paper presents a method for simulating compressible two-phase flow by combining the best features of a front tracking method (FT) and a ghost fluid method (GFM). In contrast to GFM, a Riemann problem is solved to find the ghost states. And in contrast to FT, the front states used in the Riemann problem are not dynamic variables but are obtained by extrapolation from the interior (grid) states. Pressure jumps associated with surface tension forces are modeled in the Riemann problem. This method handles surface tension forces in a sharp way and avoids artificially spreading surface tension forces over the computational grid as used in continuous surface models. To handle the topological bifurcations of a three-dimensional (3D) surface mesh in the FT, an improved locally grid-based method (LGB) is proposed. The method is robust and minimizes the numerical mass diffusion due to interface reconstruction. The performance of the method is assessed from a broad set of test problems including compressible Kelvin-Helmholtz instabilities, parasitic currents, drop oscillation, bubble-shock interaction, and Rayleigh instabilities. The proposed new method is shown to be comparable to either of its constituent methods by themselves. The advantage of the new method lies in the removal of late time instabilities associated with both of the constituent methods when applied to the 3D simulation of a high speed jet.