With accurate interaction potential surface, Be-CO Hamiltonian equation is solved by numerical methods. Cold collision dynamics for Be atom and CO molecule is investigated by quantum scattering calculations. Influence of applying electric field on elastic and inelastic collisional cross-sections of low-field-seeking state at cold and ultracold temperatures are explored. It provides theoretical support for experimental sample molecules.

We propose a new method for compressible multi-component flows with Mie-Gruneisen equation of state based on mass fr action. The model preserves conservation law of mass, momentum and total energy for mixture flows. It also preserves conservation of mass of all single components. Moreover, it prevents pressure and velocity from jumping across interface that separate regions of different fluid components. Wave propagation method is used to discretize this quasi-conservation system. Modification of numerical method is adopted for conservative equation of mass fraction. This preserves the maximum principle of mass fraction. The wave propagation method which is not modified for conservation equations of flow components mass, cannot preserve the mass fraction in the interval[0,1]. Numerical results confirm validity of the method.

Based on Eulerian ADER scheme,we build a 1D,one-step,conservative,high-order accurate,Lagrangian ADER(LADER) scheme.Main procedures of r-th order LADER scheme include:Deducing integral form of the equations in Lagrangian framework from Euler equations,using WENO reconstruction method to reconstruct conserved variables and their spatial derivatives up to (r-1)-th order on interface of mesh with high-order accuracy,evaluating Godunov values of conserved variables and their space derivatives in Lagrangian framework,computing time material derivatives of conserved variables,approximating time-integral average of physical flux function with high-order accuracy at last.Simulation of smooth regions shows that LADER scheme achieves desired accuracy and examples of discontinuous regions show the scheme is essentially non-oscillatory near discontinuities.

We propose a method of time step for predicator-corrector scheme of Lagrangian method on stagger grids.It is different from CFL time step based on tradional stable theory.The method considers nonlinear effect of original partial differential equations,and gives an adaptive time step based on physical quantities positivity preserving.Numerical results confirm validity of the method.

We study relation of chemical energy and equation of state of plane detonation,and obtain the plane detonation shock equations and CJ eonditons.Detonation relations depending on curvature are gained with coordinate transformations of one-dimensional eylindrincal fluid dynamics equations.And at the same time we get a general sonic condition.Based on pressure and temperature equillibrium in reaction zone.we get relations between velocity of detonation and curvature of PBX9404 and PBX9502 as equations of state of products and reactants and reaction rates 8re known.As experiment data of explosive are known.tlIe method can be used to adjust parameters of equations of state and reaction rates.

Assuming that detonation normal velocity is a linear function of curvature,we study propagation of detonation front on unstructured quadrilaterals with level set method.Convection term in leve set equation is solved by positive scheme,and curvature term is solved by Galerkin isoparametric finite element method and semi-implicit time stepping.On Cartesian meshes and random meshes,the scheme of level set equations containing curvature is more than first order accuracy in L₂ and L_∝ norms.Examples of nonsmooth level sets shortening and three detonation fronts colliding show that the schemes can be used to simulate propagation of detonation front on curvature.

We develop a conservative piece-wise parabolic advecting remapping method(PPRM).The first part of it is an alternate sweeping average method(ASAM) for improving symmetrization of advecting remapping method.The second part is a piece-wise parabolic distributing function for improving order.We use one-and two-dimesional examples to test order and symmetrization of PPRM.

We investigate numerically refraction of shock waves at ferrum-beryllium (Fe-Be) interface. Equations of state for Fe and Be adopt "stiffen gas" formulas. A shock polar theory is employed to analyze critical angles of transition from regular refraction to irregular refraction. A shock-capturing method in finite volume scheme with two order of precision and wave propagation is employed to discretize and solve hydrodynamics equations of shock waves. For regular refraction, numerical results agree well with shock polar theory. For irregular refraction, precursory refracted shock waves are observed, and refraction images vary with shock intensity and incident angles.

A Godunov-type ALE (Arbitrary Lagrangian-Eulerian) method based on finite volume technique is developed to simulate compressible multimaterial flows with large deformation.The method adapts well to Lagrangian,ALE or Eulerian formulations due to its arbitrary moving speed of meshes.Numerical features are studied in the formulations.Numerical traits of several Godunov-type schemes are studied.Resolutions of scheme for shock and contact are compared.

We analyze unphysical grid distortion caused by one-point quadrature in 4-node isoparametric finite element computer program.It is concluded that the rank deficiency of stiffness matrix results in hourglass distortion.A method that controlls hourglass distortion by eliminating rank deficiency is developed and validated by patch tests.

It presents numerical computation results of the refraction of a plane shock wave at the different interfaces. The unsteady, two-dimensional, compressible, Euler equations are solved numerically assuming stiffened gas equation of state. The numerical method used is PPM (Piecewise Parabolic Method) method for multi-component. On basis of solving the Riemann problem using two-shock approximation the interface can be determined by computing the volume-fraction in terms of the high-order PPM method in the whole computational field. This method is also used to compute some case of the inter-action when the shock wave meets the interfaces of the different fluids. It also gives the evolvement of interfaces due to baroclinic effects on the interface, especially in the cases of strong shock striking at the interfaces.

Two-dimensional compressible flow field for the interaction of shocks with cylinder interface is directly simulated by using Ghost Fluid method (Ghost) and γ-model method, respectively, with the same discrete order in space and time. Numerical results are compared with the experimental results. They are almost alike in the beginning time and show the right position of interface, right strength and velocity of shocks. With the time developing, the effect of large numerical dissipation of γ-model method becomes greater and greater while the low numerical dissipation of Ghost method makes it efficient to simulate the moving interface well. Comparison with experiments proves that Ghost method is better than γ-model method in simulating the problem of interface instability.

An approach combining the fifth Upwind Compact Difference Scheme and Group Velocity Control is applied to simulate directly the interaction of shocks and the density stratified interface of light-gas cylinder.Some research about the generation and development of vorticity and the distortion of edge of cylinder is done.The instability of cylinder density-interface is analyzed.Main character of the linear developing phase is that the gas of higher density goes into the one of lower denstiy at a constant velocity and the spike structure is formed and the character of the nonlinear developing phase is that a pair of vortex structures rotating adversely are formed on both sides of the top of the spike.The numerical solution accords with the experiment.