To improve finite difference scheme, Fourier analysis is used to optimize dispersion and dissipation of WENO scheme. And optimal linear weights are given. A class of hybrid schemes is designed by combing optimized WENO schemes with monotonicity-preserving scheme. A weighted hybrid WENO scheme(H-WENO) is obtained. The scheme is tested with one-dimensional shock tube problem, Shu-Osher problem, two-dimensional Mach reflection problem and R-T instability problem. It shows that the scheme has strong ability to capture shock wave and high resolution for small scale wave structure, which is improved obviously compared with original WENO scheme.

With semi-classical approximation, thermodynamic properties of Fermi gas trapped in both gravity field and magnetic field are studied. By using theoretical analysis and numerical simulation, influence of gravity field on thermodynamic properties of the system in strong magnetic field is analyzed. It shows that, compared with the case of strong magnetic field only, gravity field makes the energy, chemical potential reduced. With rising temperature, influence of gravity field on chemical potential is gradually enlarged. There is a maximal influence of gravity field on heat capacity. Gravity field makes oscillation of heat capacity almost unchangeable while oscillation center of chemical potential shift down.

Soliton dynamics is simulated for trans-polyacetylene single-chain systems using the Su-Schrieffer-Heeger (SSH) model with an additional part to include an external electric field. It is shown that the soliton moves along the chain with a constant speed when an external electric field is applied.