I wanna define nonreflecting boundary condition for numerical simulation on wall. I know we can absorb wave with porous wall but i wanna define a boundary condition which absorb shock wave without mass diffusion. Do you have any experience about it? could you please help me about it. I try some numerical method such as characteristic method, .. but when i defined it,it reflect shock waves.

Have a look at the articles by K.W. Thompson: Time dependent boundary conditions for hyperbolic systems I & II ...

Look a sponge-layer approach. It was pretty straightforward compared to characteristic methods. Good luck!