Abstract: We present a second order cell-centered finite volume method of 2D Lagrangian hydrodynamics based on semi-discrete framework.Velocity and pressure on vertex of a cell are computed with characteristics theory,Then,they are used to compute numerical flux through cell interface by trapezoidal integration rule.With a reconstruction procedure,the method is extended to second order.Several numerical experiments confirm convergence and symmetry of the method.The method permits large CFL numbers and can be applied on structured and unstructured grids.It is robust in multi-material flow simulations.

Key words: 2D Lagrangian hydrodynamics, eharacteristics theory, cell-centered scheme, second order