The VOF method is well settled. There are some algorithms as LIC, PLIC, CICSAN, for example. Level-set formulation in multiphase flows is in development and for me, there are  some issues with the formulation mainly regarding to mass conservation. But has the advantage to be a fast  method to define the interface based on an analytical function.  Immersed boundary is very smart, but in dispersed flows with a lot of particles, I do not know how computational effort is need or even if is feasible. 

There is also the SPH model, an interesting method largely used in  graphical computation and in animation as in MAYA  and 3D Studio MAX  or some plugins as RealFLow or FumeFX ( it was used in the movie 2012 in the Yellowstone volcano eruption), but is able to work to analyse real physical problems. It was firstly develop  to star and galaxy dynamics.

The two fluid model has the better performance, but is highly dependent on the  closure models (drag, lift, virtual mass forces, for example) and more  expensive on computational time when compared with the previous models. And without forget the  Lattice-Boltzmann approach that woks very well in many  situations. 

I think that  any of them is a good tool when you use inside of its limits and with knowledge of advantages and issues. 

Recently I've published a new approach to closure the interfacial force in the two-fluid model.

Bests!

Article A two-fluid model with a tensor closure model approach for f...

Dear Leonard,

VoF method is usually very effective for break-up and coalescence of many particles since this can naturally be captured however, there are some issues for accurate calculation of curvature to calculate surface tension forces. Level-set does a better job here but treating coalescence/break-up is complicated specially in 3D. Mixture of the two has been suggested in some publication to overcome these issues.

I "think" Immersed free surface is a method to effectively combine a free interface method (a VOF or Level-Set method) with rigid surfaces (for example a variation of Immersed boundary methods). For example to simulate the motion of a rigid particle on the water-air interface including the capilary forces etc.

Sina

The VOF method is well settled. There are some algorithms as LIC, PLIC, CICSAN, for example. Level-set formulation in multiphase flows is in development and for me, there are  some issues with the formulation mainly regarding to mass conservation. But has the advantage to be a fast  method to define the interface based on an analytical function.  Immersed boundary is very smart, but in dispersed flows with a lot of particles, I do not know how computational effort is need or even if is feasible. 

There is also the SPH model, an interesting method largely used in  graphical computation and in animation as in MAYA  and 3D Studio MAX  or some plugins as RealFLow or FumeFX ( it was used in the movie 2012 in the Yellowstone volcano eruption), but is able to work to analyse real physical problems. It was firstly develop  to star and galaxy dynamics.

The two fluid model has the better performance, but is highly dependent on the  closure models (drag, lift, virtual mass forces, for example) and more  expensive on computational time when compared with the previous models. And without forget the  Lattice-Boltzmann approach that woks very well in many  situations. 

I think that  any of them is a good tool when you use inside of its limits and with knowledge of advantages and issues. 

Recently I've published a new approach to closure the interfacial force in the two-fluid model.

Bests!

Article A two-fluid model with a tensor closure model approach for f...

Enjoyed reading the answers. Does any one have any views or experience of modelling free surface flow of suspension on thin porous substrate? We are looking at a problem where we want  to do numerical simulation of the spreading of a suspension on a membrane...

I think that superficial tension  plays a role in this problem. Lattice Boltzmann Method can deal with that in pore scale and wall-interface interaction . But VOF or Euler-euler approach can work with superficial tension. 

Dear Ricardo Vicente de Paula Rezende

Do you know good refs in comparison of VOF various methods like SOLA- , NASA- etc.?

Regards.