A local discontinuous Petrov-Galerkin method for numerical simulation of two kinds of air pollution models is constructed. Firstly, air pollution model equations are transformed into equivalent first-order differential equations with variable substitution. Secondly, discontinuous Petrov-Galerkin method is used to solve the differential equations. The method can choose different test function and trial function space, and maintains advantages of the intermittent Petrov-Galerkin method. Compared with local discontinuous finite element method, calculation formula of the method is simpler. Numerical examples show that the method has third-order accuracy and less error than the finite volume method. The algorithm provides a practical tool for numerical simulation of air pollution models.

Magnetic dynamic properties of Fe nanorings with small defects were simulated with Monte Carlo method. It is found that hysteresis loops of small defect Fe nanoring have "bistable" characteristics, which is consistent with experimental results. Energy research shows that vortex states appear in the region of local energy minimum. Remanence of defect system changes with defect location: The remanence increases first and then decreases with the increase of Y, and remains relatively stable in the middle region. Spin configuration of the system explains the above phenomenon well.

Theoretical analysis and numerical simulation are conducted to investigate basic properties of two-dimensional disordered disk system under quasi-static isotropic compression. Some basic concepts such as average reduced overlap, reduced pressure are introduced. Via micromechanics analysis, we deduce functional relation between reduced pressure and statistical quantities of disk system. Based on numerical simulation, variations of physical quantities such as excess average contact number, average reduced overlap, reduced pressure with excess volume fraction are studied. An approximate formula of reduced pressure is presented. These simulation results show that mechanical responses of compression are different as disk system is far from or near critical jammed state.

Numerical simulation is conducted to investigate two-dimensional frictionless disks under isotropic compression.Results with different simulation conditions are contrasted.It shows that monodisperse system is easier to crystallize.Its critical packing fraction φ_C and critical mean contact number Z_C are larger than bidisperse system.On J point,relations of packing fraction increment Δφ to mean contact number increment ΔZ and average overlap δ are almost irrelevant to simulation conditions.Relation of pressure P and packing fraction increment Δφ is only determined by interaction form.These relationships can be fitted very well by power functions.

Discrete element method is used to study probability distribution of tangential forces in granular system with composition disorder.Primary tangential force and secondary tangential force are distinguished and their statistics are analyzed separately.As the rate of defects increases,tangential force distribution transforms from approximate normal distribution to a distribution with two peaks.Finally it becomes a distribution with one peak.Whereas secondary tangential force distribution is always exponential.It shows that force distribution of composition disorder with great defect rate and structural disorder are similar.

A model of planar disc pile is applied to complicated granular matters.We analyze force transfer in the disc pile.Numerical simulation shows that the pressure on the cylinder bottom saturates with increasing height of granules.The rule of the planar disc pile is extended to three-dimensional granules and the relation between the height Z of granules and the average pressure p on cylinder bottom is obtained.

An alternating direction implicit (ADI) method for solving the two-dimensional time-dependent photon diffusion equation is studied. Numerical comparisons with analytical solution and the results of Monte Carlo simulation are achieved. Numerical results show that the method has high accuracy and good stability.

Main processes involved in the laser-target coupling are described,including the absorption of laser light,heat conduction of electron,plasma motion,nonequilibrium ionization,laser X-ray conversion and the radiation transport.It outlines the numerical simulation,presenting the partial differential equations,constructing the finite difference schemes and describing the solving methods.Finally,some calculated results are given.

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.

The paper presents the main processes of physics and the outline of the computational program related laser X-ray conversion, gives the typical pictures and numerical results. Based on numerical simulations, the laws of some important properies of physics are obtained, the results estimated by the scaling lasw are in comparison with the measurement values, they are coincident each other on quantitative tendency and quantitative results.