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Direct numerical simulation of two phase flows with adaptive mesh refinement

The object of this thesis was to study the direct numerical simulation of two phase, incompressible, isothermal immiscible flows with the adaptive mesh refinement technique. The Navier-Stokes equations are solved by an explicit projection method. The interface tracking is realized via Level Set method. The Ghost Fluid method used for the jump conditions allows the coupled resolution of the two fluids. The adaptive mesh has been implemented by the use of the PARAMESH package. This package builds a quad-tree like structure of mesh blocks of different cell size, which are recursively bisected in each direction. The blocks share the same number of cells, allowing an efficient workload balance among the available processors. A set of numerical tools have been developed to assure the correct resolution of the equations, starting from an elliptic solver, a fast and robust multigrid preconditioned BiCG-stab solver. The code has been proven on a set of academic test cases to maintain the fine mesh accuracy. The performances in terms of adaptive mesh and parallel speed-up have been shown as well. The code has finally been applied to the primary atomization of a liquid sheet sheared by two parallel high speed air flows. Results showed the capability to capture physical phenomena as the longitudinal sheet oscillation, and the ability to perform multi scale computations, which allow simulations with conditions closer to the actual injectors.