what is the difference of front tracking and immersed boundary method. I felt that they are the same or almost the same. is it right?

thanks

Front tracking method is implemented in the Lagrangian mesh method while IBM(immersed boundary method) might be in the Eulerian mesh method. Front tracking method can provide one a sharp interface tracking. IBM treats the discontinuities by some manipulation of discontinuous parameters in the Eulerian mesh. Two methods are a type of sharp interface treatment technique but they are implemented either in the Lagrangian or the Eulerian mesh, respectively.

Aboves are what I have known.

Thank you very much But waht is difference of Lagrangian and Eulerian mesh? Does the Lagrangian mesh use Lagrangian method, Eulerian mesh use Eulerian method?

Yes. That is the view of mesh motion.