Direct and Homogeneous Numerical Approaches to Multiphase Flows and Applications Roman Samulyak 1 , Tianshi Lu 2 , and Yarema Prykarpatskyy 1 1 Center for Data Intensive Computing, Brookhaven National Laboratory, Upton, NY 11973, USA {rosamu, yarpry}@bnl.gov 2 Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY 11794, USA tlu@sunysb.edu Abstract. We have studied two approaches to the modeling of bubbly and cavitating fluids. The first approach is based on the direct numeri- cal simulation of gas bubbles using the interface tracking technique. The second one uses a homogeneous description of bubbly fluid properties. Two techniques are complementary and can be applied to resolve diffe- rent spatial scales in simulations. Numerical simulations of the dynamics of linear and shock waves in bubbly fluids have been performed and com- pared with experiments and theoretical predictions. Two techniques are being applied to study hydrodynamic processes in liquid mercury targets for new generation accelerators. 1 Introduction An accurate description of cavitation and wave propagation in cavitating and bubbly fluids is a key problem in modeling and simulation of hydrodynamic pro- cesses in a variety of applications ranging from marine engineering to high energy physics. The modeling of free surface flows imposes an additional complication on this multiscale problem. The wave propagation in bubbly fluids have been studied using a variety of methods. Significant progress has been achieved using various homogeneous descriptions of multiphase systems (see for example [1,2,13,15] and references therein). The Rayleigh-Plesset equation for the evolution of the average bubble size distribution has often been used as a dynamic closure for fluid dynamics equations. This allows to implicitly include many important physics effects in bubbly systems such as the drug, viscosity, and surface tension. Numerical simu- lations of such systems require relatively simple and computationally inexpen- sive numerical algorithms. Nevertheless, homogeneous models cannot capture all features of complex flow regimes and exhibit sometimes large discrepancies with experiments [13] even for systems of non-dissolvable gas bubbles. Homogeneous models are also not suitable for modeling phase transitions in bubbly fluids such as boiling and cavitation. M. Bubak et al. (Eds.): ICCS 2004, LNCS 3039, pp. 653–660, 2004. c  Springer-Verlag Berlin Heidelberg 2004