Fourier property of nonlinear weights and limiters in wave-space are analyzed. Firstly, a statistical method is designed to analyze Fourier property of nonlinear weights. Secondly, averaged values and deviations of nonlinear weights are shown, and values with change of wave-number are analyzed. It is helpful to comprehension of nonlinear schemes. The method is a guidance for designing shock-capture schemes.

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.

Mesoscale responses of plastic boned explosives (PBX) and grannular HMX under shock loading were investigated with discrete element method(DEM). It shows that for shocked grannular HMX temperature and pressure in grain boundary are much higher than those of inner HMX crystals. In the case of shocked PBX high temperature and pressure regions are mostly located in binder and near parts. Comparisons show that temperature and pressure in grain boundary are effectively reduced by binder.

Discrete element method combined with undiffused two-phase transition model,thermodynamic consistent Helmholtz free energy function,and phase transition kinetics of relaxation equation are used to simulate α-iron phase transition process.Through simulation of phase boundary,Hugoniot relation and free surface velocity profiles are obtained.Wave interaction in loading and unloading process under different pressures is analyzed.Characteristics of loading and unloading wave velocity are acquired.

A two-dimensional elastic plastic hydrodynamics Eulerian code MEPH is applied to simulate micro-jet formation and penetration process of void in sample during shock loading.We focused on forming process of micro-jet.Maximal penetration depth versus key factors such as shock pressure and void diameter is analysed.Theoretical jet penetration is compared with numerical simulations of maximal penertration depth.

A second order least squares volume of fluid interface reconstruction algorithm with 81 cells in mesh stencil is introduced.The algorithm is compared with Youngs algorithm and a second order least squares volume of fluid interface reconstruction algorithm with 125 cells in mesh stencil.L^∞ criteria function in three dimensions is used to measure stationary interface reconstruction errors.Stationary and advecting tests show that the algorithm can track any oriented plane exactly and it is second order accurate.Compared with second order least squares volume of fluid interface reconstruction algorithm with 125 cells in mesh stencil,calculation amount of the algoritm is much smaller.Thus CPU time is saved and computing efficiency is improved.

We describe a problem that the multifluid dynamic equations are not closed.To solve equations,they must be closed.Existing closing relations are analyzed and an adaptive closing relation method according to sound velocity is given.Numerical example shows that pressure relaxation is also important for pressure equalization in mixed cells.

A two-dimensional elastic and plastic hydrodynamics code MEPH is applied to simulate ejecting process. We focus on the effect of shock pressure and shock risetime on mass ejection from shocked aluminum. It shows that with increase of shock pressure the ejecting factor keeps increasing, but the ejecting factor is not sensitive to the shock pressure. The effect of shock risetime on the mass ejection from shocked aluminum is also investigated. Numerical results agree well with experiments. The mass ejection is sensitive to shock risetime.

A fourth-order combined compact upwind (CCU) finite difference scheme with high resolving efficiency is proposed. A high-order compact difference algorithm for Navier-Stokes (NS) equations based on projection method is developed with CCU scheme on staggered grids. Convection terms are discretized by CCU scheme. Viscous terms, pressure gradient terms and pressure Poisson equations are discretized with fourth-order compact symmetric finite difference schemes. Numerical examples validate capability of the proposed approach. It is shown that the method is accurate and robust, and is applicable to complex fluid flows.