Abstract: Abstract] 2-D and 3-D numerical simulation methods of filamentation instability in laser-target interaction are presented.The Landau-fluid models are adopted with a simplified 3-D numerical method,it simulates filamentation process for laser beams in underdense plasma.Plasma background resulted by 1D simultaneously calculation of the laser-target coupling is used to investigate the filamentation process and several reasonable results have been obtained.Nonlinear and relativistic modification of transport coefficients,and nonlinear hydrodynamics computation prove to be needed for the case of intense laser beams.

Key words: filamentation, underdense plasma, numerical simulation