An HLLC-type approximate Riemann solver is proposed to simulate one-dimensional elastic-perfectly plastic flow with Wilkins model. This Riemann solver introduces plastic wave and has the same wave number with actual physics. The wave speed is determined by characteristic analysis of wave system. The algorithm is simple to implement and does not need iteration. In order to reduce wall heating error in the simulation for strong shock (or rarefaction), wall heating viscosity is designed to effectively suppress the non-physical wall heating phenomenon.

In cell-centered Godunov method,unphysical overheating problem exists in rarefaction flows.We develop a Godunov method with staggered Lagrangian discretization which is applicable to isentropic flows. Velocity and thermodynamic variables are defined in staggered discretization. The velocity averaging process in a cell is avoided,so that the kinetic energy dissipation due to the momentum averaging process is removed. In contrast to the traditional von Neumann staggered grid method, the face flux is provided by a node multidimensional Riemann solver. The difficulty in selecting multidimensional artificial viscosity is overcome. In order to reduce unphysical entropy production of multidimensional Riemann solver in rarefaction problems,we give a reasonable criterion of rarefaction appearance to satisfy the thermodynamic relation. Numerical results show that the method removes overheating problem in rarefaction problems, and retains the property of accurate shock capturing of the original Lagrangian Godunov method as well.

In order to improve robustness of multi-fluid-channel scheme on average of volume (MFCAV) and overcome its artificial intervention in actual application, a new HLLCM scheme was designed on a moving mesh, which restrains non-physical mesh tangling without artificial intervention. Numerical results show that the HLLCM scheme maintains one-dimensional spherical symmetry on equal-angle-zoned grids which has better numerical effects in keeping mesh quality and energy conservation in complex applications than MFCAV scheme.

A numerical scheme and method deducing "wall heating errors" in computing problems of radially symmetric flow using Lagrangian cell-centered schemes is investigated.Relation between "wall heating error" and modified equations of difference schemes is introduced.With comparision of sound wave approximate Riemann solver and HLL Riemann solver,a new adaptive heat conduction viscosity is introduced to ameliorate "wall heating errors".Numerical experiments show that this viscosity in current scheme provides satisfactory results.

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.

In calculation of multidimensional fluid mechanics problems with numerical schemes that accurately capture contact discontinuity, perturbation near shock wave may increase dramatically. This is called numerical shock instability. In this paper numerical shock instability on shallow water equations is studied. By analyzing linear stability of several numerical schemes, marginal stability of schemes are found having close relation with numerical shock instability. According to eigenvalue analysis, a hybrid method is designed to remedy nonphysical phenomenon by locally modify the original schemes. Numerical experiments show efficiency and robustness of HLLC-HLL hybrid scheme in eliminating shock instability of shallow water equations.

A Lagrangian finite point method for one-dimensional compressible multifluids is presented.The proposed method is a meshfree numerical procedure based on a combination of interior point scheme and interface point tracking algorithm.The discretization of unknown function and its derivatives are defined only by position of the so called Lagrangian points.The interior point formulation is based on Taylor series expansion in continuous regions on both sides of a interface.Unlike most current meshfree method,a point is settled at the interface position initially.State of interface point is updated using Rankine-Hugoniot conditions at interface together with characteristics difference computation.The interface tracking algorithm is the main feature of the method.Numerical tests show that the algorithm is oscillation-free at material interfaces and accuracy of the method is demonstrated.

Evolution of front with speed dependent on curvature is considered. The speed includes both normal and tangent components. Change of total variation of propagating front depends only on derivative of normal speed about curvature where curvature is zero. The tangent speed has no influence on change of total variation.

A class of meshfree methods——finite point method on a set of two-dimensional disordered points is studied. Fundamentals of the method are established by means of directional differentials and directional differences. Formulae relating to multi-directional differentials of each order are given. Based on these formulae and with different numbers of neighboring points, five-peint formulae and less-point (two-point, three-point and four-point) formulae are derived, respectively. Solvability conditions of the five-point formulae and permissible set of neighboring points are discussed. Approximate expressions for classical differential operators on a set of disordered points are derived. It is demonstrated with theoretical analysis and numerical experiments that the accuracy of these formulae is improved as the number of neighboring points increases. These approximate formulae lay foundation for constructing computational schemes of partial differential equations on a set of disordered points. They can be applied to computational methods on unstructured meshes to increase accuracy as well.

Numerical methods for energy flux of temperature diffusion equation on unstructured grids are discussed.A finite point method(FPM) is used to get numerical formulae of energy flux based on two-point formula or three-point formula of FPM.These formulae are applicable to unstructured grids,such as arbitrary polygon and unmatched grids etc..A numerical formula is given to compute tem-peratures at grid nodes.Numerical experiments show that the discrete solutions based on two-point formula and three-point formula have second-order convergence rate even if grids distort heavily.Accuracy of the discrete solutions based on three-point formula is better than that of two-point formula.

Electron-impact excitation collision strength Ω(nl-n'l')(3≤n≤7,4≤n'≤7) among configuration-average levels for the Ni-like Ions Pb⁵⁴⁺, Au⁵¹⁺,Ba²⁸⁺,Mo¹⁴⁺,Ge⁴⁺ have been calcuated systematically using the quasirelativitic distorted-wave methods. In addition, the collision strength in high limit have been calculated. The data for the collision strength or thermally averaged rate coefficient over the whole range of energy or temperature have been evaluated by a least-squares spline fitting procedure. As a result, the collision strength with arbitrary electron energy and rate coefficient with arbitrary temperature can be determined by ten parameters.

Following the preceding paper(Ref.[I]),an improved method is presented for calculating the integrals in electron-atom colllisions by transforming the integration contours into complex plane.This method can calculate the integrals accurately not only for cases like Ref[I],but also for the case of"nearly degenerate"which cannot be calculated by methods given in Ref[I].The caleulational accuracies have been compared and checked to be very high.

In electron-atom (or ion) collisions, it is unadvoidable to compute a large number of integrals with seriously oscillatory wavefunctions. Since direct numerical integration are very exhausted and often may fail to reach the required accuracy, analytical methods are necessary. In this paper an improved method is presented for calculating integrals with seriously osillatory in tegrands. The accuracy of phase calculation is improved for the case of wavenumber being different. The analytical expressions of integrals are given for the case of wavenumber being equal. The accury of simulation results are very satisfactory.

The problem of the slow convergence has been resolved in partial wave expansion for the excitations of electron-ion collisions, with three approximations including plane wave, coulomb Bethe and equimultiple decrease series. As an example, we have computed some important transitions of Ne-like Ge ion and made comparisons between the results obtained by three approximations. The results slow-that all the three methods are acceptable.