A barycentric Lagrange interpolation collocation method is proposed to solve the three-dimensional and four-dimensional wave equations. Firstly, the barycentric Lagrange interpolation method is introduced and the matrix format of the collocation method is given. Secondly, the solution function and initial boundary conditions of the wave equation are approximated by Lagrange interpolation. The discrete equation is obtained by collocation method, and the matrix expression of the wave equation is obtained. Finally, the initial and boundary conditions of the wave equation are imposed by the addition method and the replacement method respectively. Numerical examples show that the barycentric Lagrange interpolation collocation method has high computational accuracy and efficiency.

Molecular dynamics simulation is used to simulate response of nonlinear sinusoidal alternation flow of helium gas oscillation in a pulse tube. Formation of axial pressure wave and temperature field inducted by gas oscillation was studied.Influence of length to diameter ratio on temperature difference and phase of cold and hot ends of the pulse tube is shown. It shows that the pressure wave,speed wave and mass flow wave accompanying by driving force are similar to a sinusoidal function while the temperature wave is similar to a half-sinusoidal function. The oscillation period is shortened with increase of the diameter of the tube and prolonged with increase of the length of the tube. The maximum temperature difference between hot end and cold end increases with the length of the tube but independent of diameter. It is predicted that there is an optimal aspect ratio and oscillation period for pulse tube with different diameter, which increases with increasing of the diameter. It provides a theoretical basis for optimizing efficiency of pulse tube.

A multiscale deep learning model is proposed for fluid flow in porous media. The method is formulated on hierarchical grid system, that is, a coarse grid and a fine grid. Deep learning network is used to train data on the coarse gird. Source term and permeability field is treated as input parameter and coarse-scale solution is treated as output parameter. We construct multiscale basis functions by solving local flow problems within coarse gridcells. Heterogeneity and interactions between matrix and fracture are captured by basis functions. Oversampling technique is applied to get more accurate small-scale details. Numerical experiments show that the multiscale deep learning model is promising for flow simulation in heterogeneous and fractured porous media.

A first-principles implicit simulation program, Implicit Stratonovich Stochastic Differential Equations (ISSDE), is constructed for stochastic differential equations which describes plasmas with Coulomb collision. Basic idea of the program is stochastic equivalence between Fokker-Planck equation and Stratonovich SDE. Implicit discrete method guarantees numerical stability and conservation of kinetic energy. ISSDE is built with C++ language, and is designed to possess standard interfaces and extendible modules. Slowing-down processes of electron beams in both unmagnetized and magnetized plasmas are studied, which shows correctness of ISSDE. It provides a powerful tool for collisional plasmas studies.

Asymmetric vertical cracks in process of pressure was studied. Based on principle of seepage mechanics, well-test mathematical model, which is asymmetric finite-conductivity vertical fracture with three different outer boundary conditions, was established according to point source function and Green function. Typical curves were obtained with Laplace integral transformation and Stehfest numerical inversion. It shows that typical curve is divided into four flow stages, stage of wellbore storage,1/4-slope bilinear flow, 1/2-slope linear flow and 0.5-value horizontal line radial flow. Asymmetric factors affect mainly end time of bilinear flow stage. The greater the asymmetry factor is, the sooner the bilinear flow stage ends is. The greater the conductivity capability of fracture is, the more unobvious characteristic of pressure derivative curve of bilinear flow stage are. The bigger asymmetric factor is,the more uneven rate distribution of asymmetric fracture is. The model provides theoretical basis for well test analysis of asymmetric finite-conductivity vertical fracture.

Two-dimensional density distributions of dense plasmas in laser confinement fusion are revealed with proton imaging. Simultaneous iterative reconstruction algorithm (SIRT) is used to study influence factors of two-dimensional plasma density reconstruction. Effects of plasma density gradient, magnitude of density and initial proton energies on reconstruction errors are investigated. Importance of figuring out rough area and range of simulated plasma zone before simulation is analyzed. Furthermore, an analytical expression between reconstruction errors and noises is established through data analyses.

A locally conservative Galerkin (LCG) finite element method is proposed for two-phase flow simulations in heterogeneous porous media. The main idea of it is to use property of local conservation at steady state conditions to define a numerical flux at element boundaries. It provides a way to apply standard Ga/erkin finite element method in two-phase flow simulations in porous media. LCG method has all advantages of standard finite element method while explicitly conserving fluxes over each element. Several problems are solved to demonstrate accuracy of the method. All examples show that the formulation is accurate and robust, while CPU time is significantly less than mixed finite element method.

With a fifth-order weighted compact nonlinear scheme(WCNS-E-5),flow field of a 65° delta wing with sharp leading edges at high angles of incidence is simulated.The target is checking WCNS's ability for vortex flow at high angles of incidence and vortex breakdown location with shock-vortex interaction.We focus on sudden jump in breakdown towards apex.Unsteady Reynolds averaged Navier-Stokes(URANS) method is available including a high-order weighted compact nonlinear scheme and an SST turbulence model.It is shown that the high order scheme(WCNS-E-5) with minimum numerical dissipation and could capture discontinuities for high angles of incidence transonic flow of delta wing and the results are matched satisfactorily with experiments.Shock-vortex interaction in transonic freestream explains sudden movement of vortex breakdown as the angle of incidence is increased.

A stable and efficient element-free Galerkin method is proposed for steady convection-diffusion problems.In the method integrations are computed with a local Taylor expansion nodal integral technique.According to convection-dominated degree,integration nodes are adaptively shifted opposite to the streamline direction.Compared with conventional element-free Galerkin method with stabilization,the method exhibits better stability and higher efficiency in solving convection-dominated convection-diffusion problems.It is a pure meshfree method,which is independent of background integral.Moreover,the method is easy to be implemented.

With equivalent concept of single fracture,a discrete-fracture model is developed,in which macroscopic fractures are described explicitly as(n-1) dimensional geometry elements.This simple step greatly improves efficiency of numerical simulation.The model can really reflect impact of fractures on fluid flow through fractured reservoirs simultaneously.A fully coupling discrete-fracture mathematical model is implemented using Galerkin finite element method.Validity and accuracy of the model and numerical algorithm are demonstrated through several examples.Effect of fractures on water flooding in fractured reservoirs is investigated.It demonstrates that the discrete-fracture model is valid for fractured reservoirs,especially for those reservoirs in which macroscopic fractures exist.

Specific acoustic impedance of transparent liquid, sound transmitting distance of laser induced sound and laser beam waist radius are analyzed. It shows that the peak pressure, dominant frequency and energy of laser induced sound increase as specific acoustic impedance increases. The dominant frequency quickly drops in a short distance and then becomes a constant at a larger distance. Under the condition of optical breakdown, a high ratio of laser to sound energy conversion can be obtained with a large laser beam waist radius.

A muhi-component mathematical model characterizing polymer enhanced foam flooding filtration is established with mass conservation principle of foam components. Considering combination of foam generation, coalescence and migration phenomena, the model effectively reflects mechanism of oil phase foam coalescence and polymer foam stabilizing. Differential numerical solution is conducted with adaptive implicit method. Validity of the mathematical model is verified with experiment. Meanwhile, taken foam flooding pilot region of a oilfield, a numerical simulator is employed to study filtration characteristics of enhanced foam flooding. It is indicated that the foam system could exist stably in the formation and gradually advance to production wells to improve oil recovery.

Navier-Stokes calculation on multi-block is performed to calculate drag of the DLR-F6 wing-body configuration with CFD software TRIP2.0.Structured grids(1-to-1) and test results used are from Drag prediction workshop Ⅱ (DPWⅡ). Referenced numerical results are obtained with CFL3D. Effects of mesh density and turbulent models on aerodynamic characteristics and pressure distribution are carefully studied. Results are verified by experimental data and CFL3D results. Grid refinement leads to convergent results in SST turbulent models. It is demonstrated that turbulent models have little influence on pressure drag, but obvious influence on friction drag. The turbulent model and grid density have little influence on pressure distribution.

A method that decreases useless magnetism pressure to amplify the power of MFCG(magnetic flux compression generator) is proposed, in which the charging loop is cut off after initial current is provided.By code MFCG(V),the simulation demonstrates effectiveness of the method.

A v'²-f model,a k-ε model and an indoor zero equation model are adopted respectively to simulate mixed convections which are typical in ventilation and air conditioning systems.It indicates that there is a separated vortex near the ventilation inlet,and the accuracy for predicting this vortex is a critical factor in the simulation.The separated vortex dimension obtained by experiments is between the values calculated by the v'²-f model and the indoor zero equation model,while the dimension predicted by the k-ε model is a bit smaller.The results predicted by the indoor zero equation fit experimental results best.However,it is not in general from the view of model structure.For calculating temperature field the v'²-f model is better than the indoor zero equation model,and the k-ε model is the worst among the three.

Under a compulsive boundary condition,a simplified time-domain finite-difference beam propagation method (TD-FD-BPM) suitable for the analysis of fiber Bragg grating (FBG) is presented.In the alternating-direction implicit method (ADIM) and the generalized Douglas (GD) scheme, the time-domain beam propagation equation is discretized with a truncation error two orders lower than that of conventional finite-difference scheme.The compulsive boundary condition simplifies the boundary model,which is important in the numerical analysis of optical waveguides with open boundary conditions.We focused on the position of excitation,the shape of the pulse and its distribution in the radial direction,and the use of the one-way continuous-wave (CW) scheme.Using a modified sinusoidal pulse,a satisfactory reflective spectrum is obtained in a short symmetrical FBG through discrete Fourier transform.

The structure preservind difference algorithms for soliton equations are investigated. The symplectic structures and multisymplectic structures of the classical solitary wave equations such as the KdV, sine-Gordon and KP equations are presented to illustrate the applicability of the symplectic and multisymplectic algorithms. The concept of local conservative schemes and generalized structure preserving algorithms, which are natural generalizations of the structure preserving algorithms, are also proposed. A new concatenating method to systematically construct local conservative schemes and some numerical experiments of the constructed schemes are also presented.

A self-heating model is presented to predict the high-frequency performance of AlGaAs/GaAs heterojunction bipolar transistors (HBT's) including high current and thermal effects. A base pushout effect is discussed at high current region. And in this case, the lattice temperature, the cut-off frequency and the maximum frequency versus the collector current density are achieved.

Based on a brief description of Corrected Smoothed Particle Hydrodynamics (CSPH) method, the discretization scheme of conservation equations in axisymmetric coordinate systems is developed and a method to determine the number of particles in the computational domain is proposed. Numerical examples for hypervelocity impact are carried out and the results clearly show that CSPH is not only a suitable method for the simulation of large deformation problems in impact dynamics, but also a new method with the advantages that can not be replaced by finite element/ finite difference method.

By using explicit saturation and implicit concentration methods,numerical solution is presented to the polymer drive model characterizing dispersion and adsorption of polymer solution flowing through a porous medium.Saturation equation is solved by using an explicit total variation diminishing(TVD)method.To ensure the stability of concentration equation calculation,Crank-Nicolson difference format is used in spatial discretization,and variable is quasi-linear disposed in temporal discretization.The validity of the method presented is verified by comparison with analytic solutions.The calculated example indicates that dispersion causes dilution and dissipation of polymer solutions,and adsorption results in a loss,thus leading to lagging of concentration propagation.Also,the important polymer flooding mechanism- "oil block" is illustrated in the results of calculation.Under the condition of slug injection,the breakthrough time of oil enrichment zone lies between the breakthrough time of polymer concentration front and polymer concentration peak.

For the system in which the cylindrical mirrors of a hole-coupling plane waveguide free electron laser (FEL) oscillator are replaced by spherical mirrors, analytic estimation and numerical simulation are made respectively. It is shown that for the problem at hand, the influence on FEL by the mirror replacement is quite little.

The spatial receptive fields of simple cells in mammalian striate cortex have been characterizd as being localized,oriented,and band pass detectors.These receptive fields produced a sparse distribution of output activity in response to natural image.It shows a model of sparse coding with overcomplete basis sets in the population of simple cells from the physical process of image detection,and gives coding representation of image in realistic visual environment.

Based on the observational data of comet Hale Bopp's spiral jet structure obtained in Shanghai Astronomical Observatory from March to May 1997,the formation of the spiral jet structure is simulated by using Monte Carlo method.A basic model is proposed and the effect of different parameters is discussed.The numerical results reproduce the observed jet morphology Satisfactorily.

Since the presence of a out coupling hole alters the transverse structure of the intra cavity light in a FEL oscillator,the finite element method is used to the optical field equations and a good proximation is made for the out-coupling process in the mirror,and then some numerical results are given.It is shown that the features of the transverse structure of the intra-cavity field are well described and the numerical results are significantly improved.

The mesh dividing in an irregular domain is very difficult for computing the pulsed guide magnetic field eddy currents. A method of coordinate transformation is proposed which mappes the irregular domain to a regular domain. In the new domain it is convenient for the dividing of meshes. By using this method some satisfied computational results are obtained.

A practical method,the spectral method,is developed to find the periodic solution of non linear ordinary differentical equations directly.By expanding the solution into its Fourier series with the frequency and the amplitudes of each harmonics to be determined,the problem of sloving the non linear ordinary differential equations is transformed into the solution of corresponding non linear algebraic equations.Two examples,the van der Plo equation and the mean field equations of the neuronal groups,are also presented to explain and discuss this algorithm.

In this paper, double media of groundwater quality models of SO₄^2- and total hardness in karst area of Jian have been built and the combination of Galerkin finite element method with generalized upwind-balance scheme is presented. This method has overcomed the numerical dispersion and the vibration phenomenon. Goodness results are obtained.

The entropic increase of a plate drived by explosive has been researched in one dimension system. Usually. The high explosive is contact with a plate immediately. There is the increase entropy of in the plate resulting from the interaction of a detonation with the plate, while increasing its kinetic energy.The rather idealized problem of detonation products initially at CJ state that expands in one dimension into a void and then accelerates a plate has been analyzed in mathmatical detail. It is believed that the technique described in this report can decrease the enlropic increase and increase some kinetic energy of the plate by choosing the proper length of void and thickness of the plate.

In this paper, for a class of nonlinear system of equations #br#F₁x₁,x₂=0#br#F₂x₁,x₂=0#br# we formulate a partial Broyden method. The basic idea is that the relation of x₁ to x₂ is determined by the first subsystem of equations F₁=0, then the Broyden method is applied to the second one F₂=0, thus forming a iterative procedure.The application of partical Broyden method to discretized fpT equations is described and numerical results is given.

In this paper approximate analitical formula of current and electronic rield produced by prompt-γ photons are derived under the condition of nuclear airburst.Calculational results from those formula showed that forward position, gradient, peak value and half width of electronic field mainly depend on intensity and time behavior of prompt-γ photons released from nuclear device.