Application of the characteristic CIP method to a shallow water model on the sphere

Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the efficiency of the characteristic constrained interpolation profile (CIP) method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.

A Multimoment Finite-Volume Shallow-Water Model On The Yin-Yang Overset Spherical Grid

A numerical model for shallow-water equations has been built and tested on the Yin-Yang overset spherical grid. A high-order multimoment finite-volume method is used for the spatial discretization in which two kinds of so-called moments of the physical field [i.e., the volume integrated average ( VIA) and the point value (PV)] are treated as the model variables and updated separately in time. In the present model, the PV is computed by the semi-implicit semi-Lagrangian formulation, whereas the VIA is predicted in time via a flux-based finite-volume method and is numerically conserved on each component grid. The concept of including an extra moment (i.e., the volume-integrated value) to enforce the numerical conservativeness provides a general methodology and applies to the existing semi-implicit semi-Lagrangian formulations. Based on both VIA and PV, the high-order interpolation reconstruction can only be done over a single grid cell, which then minimizes the overlapping zone between the Yin and Yang components and effectively reduces the numerical errors introduced in the interpolation required to communicate the data between the two components. The present model completely gets around the singularity and grid convergence in the polar regions of the conventional longitude-latitude grid. Being an issue demanding further investigation, the high-order interpolation across the overlapping region of the Yin-Yang grid in the current model does not rigorously guarantee the numerical conservativeness. Nevertheless, these numerical tests show that the global conservation error in the present model is negligibly small. The model has competitive accuracy and efficiency.

Parallel Fully-Implicit Computation of Magnetohydrodynamics Acceleration Experiments

A three-dimensional MHD solver is described in the paper. The solver simulates reacting flows with nonequilibrium between translational-rotational, vibrational and electron translational modes. The conservation equations are discretized with implicit time marching and the second-order modified Steger-Warming scheme, and the resulted linear system is solved iteratively with Newton-Krylov-Schwarz method that is implemented by PETS,: package. The results of convergence tests arc plotted, which show good scalability and convergence around twice faster when compared with the DPLR method. Then five test runs are conducted simulating the experiments done at the NASA Ames MHD channel, and the calculated pressures, temperatures, electrical conductivity, back EMF, load factors and flow accelerations are shown to agree with the experimental data. Our computation shows that the electrical conductivity distribution is not uniform in the powered section of the MHD channel, and that it is important to include Joule heating in order to calculate the correct conductivity and the MHD acceleration.

A Semi-Quantitative Analysis of Essential Micronutrient in Folium Lycii Using Laser-Induced Breakdown Spectroscopy Technique

In this paper, the capabilities of laser-induced break down spectroscopy (LIBS) for rapid analysis to multi-component plant are illustrated using a 1064 nm laser focused onto the surface of folium lycii. Based on homogeneous plasma assumption, nine of essential micronutrients in folium lycii are identified. Using Saha equation and Boltzmann plot method electron density and plasma temperature are obtained, and the irrelative concentration (Ca, Mg, Al, Si, Ti, Na, K, Li, and Sr) are obtained employing a semi-quantitative method.

Study on reactive extrusion processes of block copolymer

The anionic copolymerization process of styrene-buradiene (S/B) block copolymer in a closely intermeshing co-rotating twin screw extruder with butyl-lithium initiator was studied. According to the anionic copolymerization mechanism and the reactive extrusion characteristics, the mathematical models of monomer conversion, average molecular weight and fluid viscosity during the anionic copolymerization of S/B were constructed, and then the reactive extrusion process was simulated by means of the finite volume method and the uncoupled semi-implicit iterative algorithm. Finally, the influence of the feeding mixture composition on conversion was discussed. The simulated results were nearly in agreement with the experimental results.

Numerical Analysis of Theoretical Model of the Rf MEMs Switches

An improved electromechanical model of the RF MEMS (radio frequency microelectromechanical systems) switches is introduced, in which the effects of intrinsic residual stress from fabrication processes, axial stress due to stretching of beam, and fringing field are taken into account. Four dimensionless numbers are derived from the governing equation of the developed model. A semi-analytical method is developed to calculate the behavior of the RF MEMS switches. Subsequently the influence of the material and geometry parameters on the behavior of the structure is analyzed and compared, and the corresponding analysis with the dimensionless numbers is conducted too. The quantitative relationship between the presented parameters and the critical pull-in voltage is obtained, and the relative importance of those parameters is given.

Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method.

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.

Starting Nozzle Flow Simulation Using K-G Two-Equation Turbulence Model

The starting process of two-dimensional nozzle flows has been simulated with Euler, laminar and k - g two-equation turbulence Navier-Stokes equations. The flow solver is based on a combination of LUSGS subiteration implicit method and five spatial discretized schemes, which are Roe, HLLE, MHLLE upwind schemes and AUSM+, AUSMPW schemes. In the paper, special attention is for the flow differences of the nozzle starting process obtained from different governing equations and different schemes. Two nozzle flows, previously investigated experimentally and numerically by other researchers, are chosen as our examples. The calculated results indicate the carbuncle phenomenon and unphysical oscillations appear more or less near a wall or behind strong shock wave except using HLLE scheme, and these unphysical phenomena become more seriously with the increase of Mach number. Comparing the turbulence calculation, inviscid solution cannot simulate the wall flow separation and the laminar solution shows some different flow characteristics in the regions of flow separation and near wall.

LD侧面泵浦固体激光器泵浦光分布模拟

利用Gauss光束通过光学系统的变换规律,将激光二极管阵列发出的光作为Gauss光束处理.应用矩阵光学方法,解析分析与数值模拟相结合,给出了激光二极管阵列侧面泵浦棒状固体激光介质内泵浦光的强度分布.比较了侧面环绕激光二极管阵列数量不同时泵浦光分布的均匀性;以及考虑准直系统后,不同准直透镜焦距时,晶体内泵浦光半径的大小;同时针对泵浦光在晶体内聚焦时的情况进行了简单讨论.将半解析法与光线追迹法所得结果进行了比较,二者十分相近,但前者计算要简单得多.

Band gap narrowing in heavily B doped Si1-xGex strained layers

This paper presents a comprehensive study of the effect of heavy B doping and strain in Si1-xGex strained layers. On the one hand, bandgap narrowing (BGN) will be generated due to the heavy doping, on the other hand, the dopant boron causes shrinkage in the lattice constant of SiGe materials, thus will compensate for part of the strain. Taking the strain compensation of B into account for the first time and uesing the with semi-empirical method, the Jain-Roulston model is modified. And the real BGN distributed between the conduction and valence bands is calculated, which is important for the accurate design of SiGe HBTs.

Computer simulation of reactive extrusion processes for free radical polymerization

The reactive extrusion for polymerization is an integrated polymer processing technology. A new semi-implicit iterative algorithm was proposed to deal with the complicated relationships among the chemical reaction, the macromolecular structure and the chemorheological property. Then the numerical computation expressions of the average molecular weight, the monomer conversion, and the initiator concentration were deduced, and the computer simulation of the reactive extrusion process for free radical polymerization was carried out, on basis of which reactive processing conditions can be optimized.

Free radical grafting of polyethylene with vinyl monomers by reactive extrusion

The free radical grafting of polyethylene with vinyl monomers by reactive extrusion was studied numerically. Numerical computation expressions of key variables, such as the concentrations of the initiator and polymer, grafting degree, average molecular weight and apparent viscosity, were deduced. The evolutions of the above variables were predicted by means of an uncoupled semi-implicit iterative algorithm. The monomer conversion monotonically increases with decreasing throughput or increasing initial initiator concentration; with increasing barrel temperature, the monomer conversion first increases then decreases. The simulated results are nearly in good agreement with the experimental results.

Semi-weight function method on computation of stress intensity factors in dissimilar materials

Semi-weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi-weight functions were obtained as virtual displacement and stress fields with eigenvalue-lambda. Integral expression of fracture parameters, K-I and K-II, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi-weight function method is a simple, convenient and high precision calculation method.