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.

With potential energy surface constructed in 2003, we study stereodynamics of reaction Li+HF→LiF+H using quasiclassical trajectory (QCT) method. Polarization dependent differential cross sections (PDDCSs) and P(θ_r,φ_r) distributions describing k-k'-j' correlation related to collision energies. Vibrational states and rotational states are discussed at 1.15 kcal·mol^-1-5.0 kcal·mol^-1. Furthermore, cross sections are compared with that of other calculations and experiments. It indicates that vibrational and rotational excitations have stronger impacts on PDDCSs and P(θ_r,φ_r) than collision energy. Backscattering polarization of product rotational angular momentum is positive correlated with collision energy. Cross sections agree well with results of other theories and experiments in the range of calculation collision energies.

Two kinds of Stencil elimination schemes with preserved symmetry are presented.Correlative symmetric positive definite difference equations are obtained.Condition number of coefficient matrix decreases over 7/9 folding ratio than that of five point difference Jacobi's.Their eigenvalues have a good clustered spectrum.Theoretic analysis and numerical experiments show that they are better than un-symmetric ones,and are more useful.

The discontinuous Galerkin method is developed based on high-resolution FDM and FVM.They achieve great success for solving problems in computational fluid dynamics.The basic conseption and computational scheme of the method for numerical solution of conservation laws are introduced.The order analyses and influence of the limiters are discussed by simple numerical simulations.Meantime,the numerical results of problems in hydraulic dynamic,traffic flow problems and gas dynamic problems are given.Morever,the summary of the advances in numerical applications for elliptic problems,parabolic problems and convection diffusion problems,Hamilton-Jacobi and Navier-Stokes equations are presented.

In our foregoing paper[8] we had designed a nonlinear conservative difference scheme of second-order Godunov type with piecewise-linear reconstruction,in which the slope of the reconstructed function in each grid cell can be computed by dissipating the entropy. Such a scheme satisfies the entropy condition,and computes not only numerical solution but also numerical entropy; thus, it is different from all former conservative schemes. A socalled entropy dissipator in the scheme, which dissipates the entropy in each grid cell in the computation, plays an important role in stabilizing the computation. The entropy dissipator designed in is quite complicated. In this paper, we numerically discuss why entropy must be dissipated and how much entropy should be dissipated. A new entropy dissipator, based on the second-order difference of the numerical solution is given. Numerical examples are presented to show how the entropy dissipator suppresses nonphysical oscillations near discontinuities.

Taking aluminum dust as an example, the generation and acceleration of shock wave induced by weak Ignition in dust suspension in a long horizontal combustion tube have been studied theoretically and numerically. Two fluid model and TVD technique are used to calculate the flow field of gas phase and particle phase and Arrihenius law and k-ε model considering the near wall turbulent are used to calculate the chemical reaction. The wall turbulent plays a important role in the flame acceleration and combustion induce shock process. Simulated results reveal the innate character from compressive wave to shock wave in combustible dust suspension and the flow field parameter distribution. The simulated and measured results are compared with a good agreement.

There is a restriction to the solution of the epuation of θ (the ratio between the density of the nuclear matter and the density of the nuclear matter at saturation) in the J. Cooperstein's equ ation of state. Starting from the expression of nucleons pressure near the saturation density at zero temperature, a expression of nucleon internal energy is obtained by us. the re striction mentioned above in J. Cooperstein's equation of state has been removed by substituting the expression of nucleon internal energy obtained by us for the expression used by J.Cooperstein. Me present results of hydrodynamic cal culation of core collapse and subsequent shock wave formation and propagation using the equation of state of us and using the 15M_⊙ initial model of WZW.The relesse of gravitational binding energy of core can be increased by proper softening the equation of state above the sqturation density of nucl ear matter.

The analysis contrasting the feature of BBAL's equation of state (eos) with the feature of equation of state EOS(1) is presental. At range of low density of matter(ρ<10¹¹g cm^-3), the chemical potential of neutron and proton of BBAL's(eos) differs notablly from EOS(1).This results in that two equations of state mentioned above differ greatly in abundance of free neutron and free proton at low density.The difference between the balance expression for finite temperature correct (thermal effect) and for "zero temperature appoximation" has been investegated.The effect for finite temperature correct on the chemical potential of neutron and proton is small, but the effect on the mass number and charge number of the average heavy nucleus is marked.Having taken 15M_① model of weaver et al.as initial model,the collapse process of stellar core between the onset of collapse and core bounce has been calculated by using both the (eos) of BBAL and EOS(1).The results show that the difference betwean the calculational results of stellar collapse (at ρ_c~10¹⁴g cm^-3) with EOS (1) and with BBAL's (eos)is not so large, in spite of that BBAL's (eos) differ greatly from EOS(l) in abundance of free nucleon at low density. The difference between calculational result (at ρ_c~10¹⁴g cm^-3) of stellar collapse resulting from finite temperature correct and "zero temperature approximation" for both BBAL's (eos) and EOS(l) is more notable.