In this work,we derive a series of extended hydrodynamic models from the Boltzmann transport equation(BTE)by using the Grad moment expansion and globally hyperbolic closed technique for the simulation of semiconductor device.Such models can capture the major features of the solution of BTE,and the solutions recovered from these models converge to the solution of BTE,as the order of the models increase.As a practical application for these models in semiconductor devices,where we are mainly concerned with the stationary solution,we developed a robust multigrid solver for them to further improve the numerical efficiency.Numerical simulations of the carrier transport in a silicon $n^+$-$n$-$n^+$ diode are carried out,to verify the accuracy and convergence of the extended hydrodynamic models.Numerical efficiency of the multigrid solver is also shown by these simulations.