Smoothed Particle Hydrodynamics: A consistent model for interfacial multiphase fluid flow simulations
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In this work, a consistent Smoothed Particle Hydrodynamics (SPH) model to deal with interfacial multiphase fluid flows simulation is proposed. A modification to the Continuum Stress Surface formulation (CSS)  to enhance the stability near the fluid interface is developed in the framework of the SPH method. A non-conservative first-order consistency operator is used to compute the divergence of stress surface tensor. This formulation benefits of all the advantages of the one proposed by Adami et al.  and, in addition, it can be applied to more than two phases fluid flow simulations. Moreover, the generalized wall boundary conditions  are modified in order to be well adapted to multiphase fluid flows with different density and viscosity. In order to allow the application of this technique to wall-bounded multiphase flows, a modification of generalized wall boundary conditions is presented here for using the SPH method. In this work we also present a particle redistribution strategy as an extension of the damping technique presented in  to smooth the initial transient phase of gravitational multiphase fluid flow simulations. Several computational tests are investigated to show the accuracy, convergence and applicability of the proposed SPH interfacial multiphase model.
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