An incompressible multi-phase smoothed particle hydrodynamics (SPH) method for modelling thermocapillary flow

This paper presents a novel smoothed particle hydrodynamics (SPH) model for thermocapillary flow. The formulation is valid for truly incompressible flow, and takes a variety of mechanisms into account including multiphase flow, heat transfer and surface force (particularly the Marangoni force). A sub-model for heat transfer considers the actual volume of SPH particle in the formulation, and a sub-model for Marangoni force employs a corrective smoothed particle method for the first time in the calculation of one-sided gradient of temperature. The performance of the sub-models for heat transfer and Marangoni force, and their combination with a sub-model for multiphase flow, are verified in related case studies. This incompressible SPH method is a meshless Lagrangian methodology, which is very good at modelling interfacial problems under hydrodynamic and thermal influences.