Density functional theory （DFT） B3LYP method is used to theoretically investigate the adsorption conformations of H2O and glycol on the relaxation surface of β-Si3N4（0001） with cluster models. For H2O, the most stable structure is that adsorbed through the H atom lying above a N（3） site of the relaxation surface of β-Si3N4（0001）; while for glycol, it is the one adsorbed via the H atom lying above the center of Si（2） and N（3） of the same relaxation surface. The adsorption energy, adsorption bond and transfer electrons of the two adsorbed substances prove that glycol is easy to be adsorbed on the relaxation surface of β-Si3N4（0001）.
A third-order numerical scheme is presented to give approximate solutions to multi-dimensional hyperbolic conservation laws only using modified coefficients of an essentially non-oscillatory （MCENO） scheme without increasing the base points during construction of the scheme. The construction process shows that the modified coefficient approach preserves favourable properties inherent in the original essentially nonoscillatory （ENO） scheme for its essential non-oscillation, total variation bounded （TVB）, etc. The new scheme improves accuracy by one order compared to the original one. The proposed MCENO scheme is applied to simulate two-dimensional Rayleigh-Taylor （RT） instability with densities 1：3 and 1：100, and solve the Lax shock-wave tube numerically. The ratio of CPU time used to implement MCENO, the .third-order ENO and fifth-order weighed ENO （WENO） schemes is 0.62：1：2.19. This indicates that MCENO improves accuracy in smooth regions and has higher accuracy and better efficiency compared to the original ENO scheme.
