It is proposed to develop new numerical algorithms and mathematical models predicting the breakup of liquid into droplets due to cross-flowing air and the resulting gas-liquid mixture that follows. New numerical methods are proposed which exploit large-aspect ratio computational elements. The investigator together with two graduate students, shall develop new algorithms for including the capability for large aspect ratio elements, as a part of a dynamic block-structured adaptive mesh method. The study of large aspect ratio elements as a part of an adaptive, unstructured grid framework has received significant attention recently (albeit, not in the context of two-phase flows, as we propose to study). In contrast, the study of moving mesh methods with large aspect ratio elements, as a part of a block structured adaptive framework, has received very little attention. An algorithm based on block structured adaptive mesh refinement affords one the advantage of easy scalability in regard to parallel computing, adoption of multigrid methodology and implementation of temporal sub-cycling techniques. Numerical analysis issues regarding stability and convergence of a numerical method when applied on a moving mesh, block structured adaptive grid, shall be investigated. Also, algorithms defining the motion of the moving mesh shall be investigated. It is important that the level of skewness for the moving mesh can be controlled. Research developed in this proposal can be applied to mathematical problems that exhibit moving boundary layers, shock waves, ignition fronts, or sharp interfaces. This proposal is concerned with the development of orders of magnitude faster (100 times faster) numerical tools for the simulation of multiphase flow problems as applicable to science and industry. These numerical tools shall be specifically formulated for high-density ratio, high-shear flows at an acceptable computational cost for engineering analysis of practical problems. One immediate application of the proposed research is a jet-propulsion system in which fuel injected as a liquid is atomized into spray by interaction with a gas phase. Another application is the prediction of momentum and energy transfer in the ocean due to hurricane force winds. In order to predict momentum and energy transfer at the sea surface, one must take into account the sea spray generated by the high speed winds. The ultimate benefits to society are reduced pollution, increased engine efficiency, and improved hurricane predictive capability due to a more accurate sea-spray parameterization. This proposal is motivated by interactions between the PI and industry (e.g. UTRC). Success of this proposal will not only have a direct impact on industrial applications relevant to atomization type processes, but also a direct impact on any industrial/scientific application of multiphase flow (e.g. navy ship hydrodynamics, microfluidic applications for testing human serum, biological fluid flows, nuclear reactor cooling systems, and underwater explosions). The PI has ongoing collaborations with SAIC (ship hydrodynamics), Department of Applied Chemistry at the Muroran Institute of Technology (non-newtonian multiphase flows in chemical processing applications), the Center for Bio-Imaging and Modeling at Rutgers University (CBIM, visualization and animation of multiphase flows), for which all of these collaborations benefit from the proposed research on simulating multiphase flows. The proposed research involves the participation of graduate students; graduate students shall be trained on issues which are timely and to which they have access to experts in the field.