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.

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.

It provides an overview of the parallel computing for 2-dimensional plasma simulations with particle clouds in cells methods under both shared-memory and distrbuted-memory parallel computing environments.The parallel algorithm and its implementation are desigened on the basis of the serial algorithm and the executing characteristics of the serial code.The practical parallel computations are performed under Challenge,DAWN 1000+, Power PC Cluster and XMZY. Many important conclusions are given and quite useful for the parallel computations of both types of particle simulation methods and other applicational codes.

A nine point difference scheme and iteration solving method is presented for two dimensional energy equations with three temperatures, in numerical simulation of driven implosion by laser. Some results are given as well.

Some improving works have been done on the SCF-Xα-SW and LMTO Programs by vectorization and parallelization.The energy level of C₆₀ is researched.The 108 one electrom Rydberg excitation energies of benzene,such as 1e_1g,2e_2g,1a_2u→ka_1g(k=3-11),ke_2g(k=2-7),ke_1u(k=3-8),ke_1g(k=2-5),ke_2g(k=3-5),ke_2u(k=2-3),kb_2u(k=2-3),kb_1u(k=2-3),1b_1g,1b_2g are calculated.The electronic structure and bulk modulus of some U-Ni alloys are also analyzed.

In view of the complexities of laser cavity target flow, a numerical technique is presented that couples an Eulerian approximation with a Lagrangian approximation,onedimensional calculation with two dimensional calculation. We call it EL-1D2D method. On the basis of trace interface moving grid method, some particular technique is established mainly by setting an Eulerian line and by merging the zone adaptively beside the Eulerian line. Numerical results show that this method can calculated fairly complicated flow in the cavity and get reasonable physical image.

In order to study physical laws related to laser X-ray conversion, two kinds of difference schemes, i.e.implicit method and splitting scheme, for solving electronic、ionic and photonic temperature equations are presented. The splitting scheme separating the energy exchange term from other terms is introduced and its influence on temperature is also investigated.

This paper presents a calculating method for tracing the moving phase-interface.The essential idea is that the von-Neumann numerical method is used in the region far from the phase-interface.In both sides close to phasc-interface a special difference scheme is established by using Rankine-Hugoniot jumping conditions and some characteristics of hyperbolic equations of fluid dynamics.