Compressible simulations of bubble dynamics with central-upwind schemes

This paper discusses the implementation of an explicit density-based solver, that utilises the central-upwind schemes for the simulation of cavitating bubble dynamic flows. It is highlighted that, in conjunction with the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) scheme they are of second order in spatial accuracy; essentially they are high-order extensions of the Lax–Friedrichs method and are linked to the Harten Lax and van Leer (HLL) solver family. Basic comparison with the predicted wave pattern of the central-upwind schemes is performed with the exact solution of the Riemann problem, for an equation of state used in cavitating flows, showing excellent agreement. Next, the solver is used to predict a fundamental bubble dynamics case, the Rayleigh collapse, in which results are in accordance to theory. Then several different bubble configurations were tested. The methodology is able to handle the large pressure and density ratios appearing in cavitating flows, giving similar predictions in the evolution of the bubble shape, as the reference.     

An improved MUSCL treatment for the SPH‐ALE method: comparison with the standard SPH method for the jet impingement case

In the present work, a new implementation of the Monotone Upwind‐centered Scheme for Conservation Laws (MUSCL) ‐ Hancock scheme has been developed for the SPH‐Arbitrary Lagrangian Eulerian (ALE) method. The resulting method was tested at various benchmark cases and then it was used to simulate the jet impingement on a flat plate for several different impingement angles, in comparison with the standard SPH method and results from literature. The SPH‐ALE method proves to produce higher quality results than the standard SPH method in all cases, while the MUSCL treatment tends to remedy the issues of the numerical viscosity, inherent to the method, up to a point. Copyright © 2012 John Wiley & Sons, Ltd.