Incorporation of diffuse interface in smoothed particle hydrodynamics: Implementation of the scheme and case studies

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Abstract
An algorithm is proposed to incorporate diffuse interface (DI) modelling in the Lagrangian smoothed particle hydrodynamics (SPH) for the simulation of interface and its evolution. The model assumes a smooth variation of properties across the interface of two immiscible fluids. The conventional Cahn–Hilliard equation has been adopted to take care of the property variation across the DI. However, it has been recast to be compatible with the particle‐based formulation. The momentum equation has also been modified to account for the surface energy. Three different case studies namely evolution of gas bubbles at submerged orifice, drop deformation in shear flow and deformation of droplets in parabolic flow have been selected for the application of DI‐based SPH (DI‐SPH) method of solution. For the sake of comparison the predictions have been made for all the cases by DI‐SPH as well as by the basic SPH without incorporating DI. Results of these two simulations have been compared with those already reported in the literature. In all the cases DI‐SPH shows a definite improvement in the prediction of the complex interface and their dynamics. The present work demonstrates the strength of the technique in the simulation of diverse multiphase flow problems with evolving interfaces. Copyright © 2010 John Wiley & Sons, Ltd.

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