Both of these methods are the kinds of volume tracking methods. Also, VOF is another kind of volume tracking method. These methods use different criteria for finding that which phases are placed in which cells.

LSM uses a function that describes the smallest distance from the interface as a criteria. In the first phase, this distance is positive and in another one is negative. Numerical solution of advection eq. Of the function of distance estimate the position of the interface.

In the phase-field method the criteria is a function (phase field function) of [-1,+1], that in first phase area this function is +1 and in another one is -1. Using this function the interface is where that this function is zero. This function has smooth variation, in a narrow area near the interface.

This paper can be helpful I think,

http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=1752669

Conference Paper Phase-Field Versus Level Set Method for 2D Dendritic Growth

Dear Dewaker,

If you are interested in boundaries moving either in a predefined way or freely, the level set method can be used to describe these boundaries as the (say) 0 level set of a function. The key is to relate correctly the (normal) velocity of the moving boundary to the evolution of the level set.

If you want to avoid moving boundaries and prefer expressing everything in fixed domains, you may use a phase field method. This is an additional unknown function, which is close to 1 in one sub-domain, and close to 0 (or -1) in another one - approximating the characteristic function, or the sign of the level set mentioned above. The region where the phase field changes from values close to 1 to ones close to 0 (or -1) is not an interface or a boundary (as in the case of the level set approach), but a narrow one. This is why you may see the phase field approach as one where the moving boundary is being diffused. The advantage is obvious, you work in a fixed domain and identify the moving boundaries as thin regions inside it. However, also here you have to make sure that the equation for the phase field is compatible with the sharp interface model. More precisely, if the thickness of the transition region approaches 0, which can be controlled by some parameters in the phase field model, the limit is an interface/boundary moving as in the original model. In other words, you end up with the original model, involving moving boundaries.

Good luck,

Sorin

Dear Sharma

look at this doc. in attached files

kind Regards

- level set method:

+ two phases

+ computationally less expensive (one transport equation)

+ recommended for larger scale simulations where the interface is not well resolved by the mesh and where the mean position of the interface is sought rather than the fine details.

- phase field method:

+ can solve for up to three phases.

+ allows for fluid-structure interaction and phase separation models.

+ includes more physics and it is more accurate as long as the interface is properly resolved by the mesh.

+ computationally more expensive (two additional transport equations)

+ recommended for microfluidic simulations where the surface shape is of primary importance.

Source: https://www.comsol.com/blogs/which-multiphase-flow-interface-should-i-use/

applications on comsol:

- level set method: capillary filling

- phase field method: Two-Phase Flow with Fluid-Structure Interaction