Where is the mass loss from in Level Set method? There contains two steps in Level Set, First is the advection, Second is reinitializaion. My opinion is that it is from reinitializaion.

Is it right?

>>Where is the mass loss from in Level Set method?

since zero-level set is not correct level set after advection due to numerical diffusion

>>My opinion is that it is from reinitializaion

this is reverse, reinit is away to correct level set and move it to true position, but mass loss is still present, without reinti, sitution is more severe.

solution is using high accurate HJ solvers (WENO + TVD RK) or using aided particles near zero level set to correct level set position after advection or adaptation near interface or ...

In general LS methods are neither globally or locally conservative. The simple reason is that a conserved, physical quantity (e.g., mass or volume in incompressible flow) is not advected, but rather a smooth function (the "distance" function). Conservation is therefore not inherent by design. The best "fix" to this approach is the particle-based reinitialization devised by Fedkiw. There really is "emotional involvement" in LS methods.

are "Doug Kothe", D. B. Kothe leader of Telluride project?