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This paper presents a methodology for simulation of two-phase flows with surface tension in the framework of unstructured meshes, which combines volume-of-fluid with level-set methods. While the volume-of-fluid transport relies on a robust and accurate polyhedral library for interface advection, surface tension force is calculated by using a level-set function reconstructed by means of a geometrical procedure. Moreover the solution of the fluid flow equations is performed through the fractional step method, using a finite-volume discretization on a collocated grid arrangement. The numerical method is validated against two-and three-dimensional test cases well established in the literature. Conservation properties of this method are shown to be excellent, while geometrical accuracy remains satisfactory even for

Navier-Stokes equations and mass transfer (or heat transfer) equation are discretized using a finite vol-31 ume method on a collocated unstructured mesh, whereas a multiple marker level-set approach is used 32 for interface capturing in bubble swarms. This method avoids the numerical coalescence of the fluid par-33 ticles, whereas the mass conservation issue inherent to standard level-set methods is circumvented. 34 Furthermore, unstructured flux-limiter schemes are used to discretize the convective term of momentum 35 transport equation, level-set equations, and chemical species concentration equation, to avoid numerical 36 oscillations around discontinuities, and to minimize the numerical diffusion. A convection-diffusion-37 reaction equation is used as a mathematical model for the chemical species mass transfer at the contin-38 uous phase. Because the mathematical analogy between dilute mass transfer and heat transfer, the same 39 numerical model is applicable to solve both phenomena. The capabilities of this model are proved for the 40 diffusion of chemical species from a sphere, external mass transfer in the buoyancy-driven motion of sin-41 gle bubbles and bubble swarms. Results are extensively validated by comparison with analytical solu-42 tions and empirical correlations from the literature.43

A new level-set model is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios at dynamically deformable interfaces. The Navier–Stokes equations coupled with the energy conservation equation are solved by means of a finite-volume/level-set approach, adapted to a multiple marker methodology in order to avoid the numerical coalescence of the fluid particles. The temperature field is coupled to the surface tension through an equation of state. Some numerical examples including thermocapillary driven convection in two superimposed fluid layers, and thermocapillary motion of single and multiple fluid particles are computed using the present method. These results are compared against analytical solutions and numerical results from the literature as validations of the proposed model.Peer ReviewedPostprint (author's final draft

20Keywords: 21Bubble dynamics 22Level-set method 23Multiphase flow 24