We present DG method for solving two-way coupling compressible gas-solid two-phase flow. Equations of both phases are discreted simultaneously, including convection term and source term. Splitting technique to discretize governing equations separately is avoided. Numerical flux of both phases is based on approximate Riemann solver. Dusty-gas shock tube problem with particles in low pressure section is simulated. Comparisons of equilibrium flow and frozen flow are made. Influence of particles in gas and interaction rules between two phases in relaxation zone behind shock are studied. It found that mass ratio of particles determines last equilibrium state and particles diameter determines transition process of two-phase flow from nonequilibrium to equilibrium flow. Namely, different diameter particles correspond to different relaxation time and distance. It shows that the numerical method proposed is reliable. It lays a foundation for more complicated gas-solid two-phase flow problems.

Dissipative particle dynamics (DPD) is modified by introducing attractive force. Attractive interaction of liquid and solid and micro-scale flow in nano throats is simulated to discuss mechanism of boundary layer. It is found that thermal motion affects velocity significantly in molecular scale while pressure gradient is leading function as greater than molecular scale. However, thermal motion cannot change integral moving direction. As throat radius becomes larger, parabola shape of velocity distribution becomes more and more obvious. Boundary layer thickness is affected by pressure gradient, throat radius and fluid viscosity. As pressure gradient increases and fluid viscosity decreases, boundary layer thickness decreases. As throat radius decreases, boundary layer thickness increases first and then decreases. Boundary layer is essential reason of nonlinear flow behavior and thickness of boundary layer increasing makes nonlinear flow behavior more obvious.

The bandgap structure of 2-D dielectric photonic crystals is analyzed using the method of lines(MoL).The eigenvalue equation for 2-D dielectric photonic crystals is derivated.The photonic crystals with different parameters are computed and the results are validated by FDTD and published results.The TE and TM band gaps are considered, which gives a reference to the design of dielectric photonic crystals.