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A first-principles investigation on the electronic structure, mechanical, and thermal properties of Zr-Si compounds has been investigated to prompt the development of new materials. The influence of Si content on mechanical and thermal properties is clarified. All the Zr-Si compounds are strikingly incompressible under uniaxial stress along x, y, and z axes. β-ZrSi possesses the strongest resistance to shape change and uniaxial tensions. α-ZrSi presents better performance of the resistance to volume change. The bulk modulus first increases and then decreases with the increase of the Si concentration. All the compounds exhibit brittle behavior. These zirconium silicides have relatively low bulk and shear modulus, but the shear anisotropy is strongly dependent on diverse directions. Debye temperature increases linearly with the increase of Si content. ZrSi 2 shows the best capacity of thermal conductivity. The minimum thermal conductivity in all the crystallographic directions is progressively increased with the increase of Si content except for β-ZrSi in the [010] direction.

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In this paper, the finite difference weighed essentially non-oscillatory (WENO) scheme is incorporated into the recently developed lattice Boltzmann flux solver (LBFS) to simulate compressible flows. The resultant WENO-LBFS scheme combines advantages of WENO scheme and LBFS, e.g., high-order accuracy, high resolution and physical robustness. Various numerical tests are carried out to compare the performance of WENO-LBFS and that of other WENO-based flux solvers, including the Lax-Friedrichs flux, the modification of the Harten-Lax-van Leer flux, the multi-stage predictor-corrector flux and the flux limiter centered flux. It turns out that WENO-LBFS is able to capture discontinuous profile in shock waves. Comparatively, the WENO-LBFS scheme costs less CPU time and eases programming.