  It is known that both linear and nonlinear optical phenomena can be produced
when the plasmon in metallic nanostructures are excited by the external
electromagnetic waves. In this work, a coupled system of Maxwell equations and
a gas dynamic model including a quantum pressure term is employed to simulate
the plasmon dynamics of free electron fluid in different metallic
nanostructures using a discontinuous Galerkin method in two dimensions.
Numerical benchmarks demonstrate that the proposed numerical method can
simulate both the high order harmonic generation and the nonlocal effect from
metallic nanostructures. Based on the switch-on-and-off investigation, we can
conclude that the quantum pressure term in gas dynamics is responsible for the
bulk plasmon resonance. In addition, for the dielectric-filled nano-cavity, a
coupled effective polarization model is further adopted to investigate the
optical behavior of bound electrons. Concerning the numerical setting in this
work, a strengthened influence of bound electrons on the generation of high
order harmonic waves has been observed.
