Abstract: We propose a method of time step for predicator-corrector scheme of Lagrangian method on stagger grids.It is different from CFL time step based on tradional stable theory.The method considers nonlinear effect of original partial differential equations,and gives an adaptive time step based on physical quantities positivity preserving.Numerical results confirm validity of the method.

Key words: positivity preserving, time step, predicator-corrector scheme of Lagrangian method