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.

Pull-In Instability Of Micro-Switch Actuators: Model Review

The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type micro and nano-switches. It is found that the error of the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minimal when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam's deflection, these two models not only are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to that the boundary conditions are not completely satisfied when computing the numerical integration of the deflection.

Computation of turbulent-flow in a square duct - aspects of the secondary flow and its origin

A numerical study of turbulent flow in a straight duct of square cross-section is made. An order-of-magnitude analysis of the 3-D, time-averaged Navier-Stokes equations resulted in a parabolic form of the Navier-Stokes equations. The governing equations, expressed in terms of a new vector-potential formulation, are expanded as a multi-deck structure with each deck characterized by its dominant physical forces. The resulting equations are solved using a finite-element approach with a bicubic element representation on each cross-sectional plane. The numerical integration along the streamwise direction is carried out with finite-difference approximations until a fully-developed state is reached. The computed results agree well with other numerical studies and compare very favorably with the available experimental data. One important outcome of the current investigation is the interpretation analytically that the driving force of the secondary flow in a square duct comes mainly from the second-order terms of the difference in the gradients of the normal and transverse Reynolds stresses in the axial vorticity equation.

Short-Term Nonlinear Response of Tension Leg Platform in Random Sea Waves

Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that motions (translations and rotations) are small magnitude. However, when TLP works in severe adverse conditions, the a priori assumption on small displacements may be inadequate. In such situation, the motions should be regarded as finite magnitude. This paper will study stochastic nonlinear dynamic responses of TLP with finite displacements in random waves. The nonlinearities considered are: large amplitude motions, coupling the six degrees-of-freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. The nonlinear dynamic responses are calculated by using numerical integration procedure in the time domain. After the time histories of the dynamic responses are obtained, we carry out cycle counting of the stress histories of the tethers with rain-flow counting method to get the stress range distribution.

高吸收强度下的波长调制光谱

基于洛伦兹线型近似，研究了高吸收强度下波长调制吸收光谱中谐波信号的行为。得到了二、四、六次谐波幅度与吸收强度的关系的近似解析表达式。解析表达式的结果与数值计算得到的相符合。理论分析的结果在一个用于瓦斯传感的波长调制光谱系统上得到了验证。发现各偶次谐波随吸收强度的变化不仅有最大值还有零点，这一结论对瓦斯传感器的设计具有实际意义。

Steady-state bright-dark vector spatial solitons in biased photorefractive-photovoltaic crystals

We show that bright-dark vector solitons are possible in biased photorefractive-photovoltaic crystals under steady-state conditions, which result from both the bulk photovoltaic effect and the spatially nonuniform screening of the external bias field. The analytical solutions of these vector solitons can be obtained in the case of \sigma\ much less than 1, where sigma is the parameter controlling the intensities of the two optical beams. In the limit of -1 < sigma much less than 1, these vector solitons can also be determined by use of simple numerical integration procedures. When the bulk photovoltaic effect is neglectable, these vector solitons are bright-dark vector screening solitons studied previously in the \sigma\ much less than 1 regime, and predict bright-dark vector screening solitons in the -1 < sigma less than or equal to 1 regime. When the external bias field is absent, these vector solitons predict bright-dark vector photovoltaic solitons in closed and open circuits. (C) 2002 Elsevier Science B.V. All rights reserved.

A transfer matrix approach to conductance in quantum waveguides

A transfer matrix approach is presented for the study of electron conduction in an arbitrarily shaped cavity structure embedded in a quantum wire. Using the boundary conditions for wave functions, the transfer matrix at an interface with a discontinuous potential boundary is obtained for the first time. The total transfer matrix is calculated by multiplication of the transfer matrix for each segment of the structure as well as numerical integration of coupled second-order differential equations. The proposed method is applied to the evaluation of the conductance and the electron probability density in several typical cavity structures. The effect of the geometrical features on the electron transmission is discussed in detail. In the numerical calculations, the method is found to be more efficient than most of the other methods in the literature and the results are found to be in excellent agreement with those obtained by the recursive Green's function method.

人工源频率域大地电磁法正反演研究

The CSAMT method is playing an important role in the exploration of geothermal and the pre-exploration in tunnel construction project recently. In order to instruct the interpretation technique for the field data, the forward method from ID to 3D and inversion method in ID and 2D are developed in this paper for the artificial source magnetotelluric in frequency domain. In general, the artificial source data are inverted only after the near field is corrected on the basis of the assumption of half-homogeneous space; however, this method is not suitable for the complex structure because the assumption is not valid any more. Recently the new idea about inversion scheme without near field correction is published in order to avoid the near field correction error. We try to discuss different inversion scheme in ID and 2D using the data without near field correction.The numerical integration method is used to do the forward modeling in ID CSAMT method o The infinite line source is used in the 2D finite-element forward modeling, where the near-field effect is occurred as in the CSAMT method because of using artificial source. The pseudo-delta function is used to modeling the source distribution, which reduces the singularity when solving the finite-element equations. The effect on the exploration area is discussed when anomalous body exists under the source or between the source and exploration area; A series of digital test show the 2D finite element method are correct, the results of modeling has important significant for CSAMT data interpretation. For 3D finite-element forward modeling, the finite-element equation is derived by Galerkin method and the divergence condition is add forcedly to the forward equation, the forward modeling result of the half homogeneous space model is correct.The new inversion idea without near field correction is followed to develop new inversion methods in ID and 2D in the paper. All of the inversion schemes use the data without near field correction, which avoid introducing errors caused by near field correction. The modified grid parameter method and the layer-by-layer inversion method are joined in the ID inversion scheme. The RRI method with artificial source are developed and finite-element inversion method are used in 2D inversion scheme. The inversion results using digital data and the field data are accordant to the model and the known geology data separately, which means the inversion without near field correction is accessible. The feasibility to invert the data only in exploration area is discussed when the anomalous body exists between the source and the exploration area.

Numerical simulation of an adaptive optics system with laser propagation in the atmosphere

A comprehensive model of laser propagation in the atmosphere with a complete adaptive optics (AO) system for phase compensation is presented, and a corresponding computer program is compiled. A direct wave-front gradient control method is used to reconstruct the wave-front phase. With the long-exposure Strehl ratio as the evaluation parameter, a numerical simulation of an AO system in a stationary state with the atmospheric propagation of a laser beam was conducted. It was found that for certain conditions the phase screen that describes turbulence in the atmosphere might not be isotropic. Numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree well with those computed by means of an integration method. However, the computer time required for the FFT method is 1 order of magnitude less than that of the integration method. Phase tailoring of the calculated phase is presented as a means to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time to our knowledge that for a constant delay time of an AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. This finding indicates that the better compensation capability of an AO system does not mean better correction effectiveness. (C) 2000 Optical Society of America.

Direct numerical simulation of transition and turbulence in compressible mixing layer

The three-dimensional compressible Navier-Stokes equations are approximated by a fifth order upwind compact and a sixth order symmetrical compact difference relations combined with three-stage Ronge-Kutta method. The computed results are presented for convective Mach number Mc = 0.8 and Re = 200 with initial data which have equal and opposite oblique waves. From the computed results we can see the variation of coherent structures with time integration and full process of instability, formation of Lambda-vortices, double horseshoe vortices and mushroom structures. The large structures break into small and smaller vortex structures. Finally, the movement of small structure becomes dominant, and flow field turns into turbulence. It is noted that production of small vortex structures is combined with turning of symmetrical structures to unsymmetrical ones. It is shown in the present computation that the flow field turns into turbulence directly from initial instability and there is not vortex pairing in process of transition. It means that for large convective Mach number the transition mechanism for compressible mixing layer differs from that in incompressible mixing layer.

Numerical analysis of spatial evolution of the small signal gain in a chemical oxygen-iodine laser operating without primary buffer gas

A chemical oxygen iodine laser (COIL) that operates without primary buffer gas has become a new way of facilitating the compact integration of laser systems. To clarify the properties of spatial gain distribution, three-dimensional (3-D) computational fluid dynamics (CFD) technology was used to study the mixing and reactive flow in a COIL nozzle with an interleaving jet configuration in the supersonic section. The results show that the molecular iodine fraction in the secondary flow has a notable effect on the spatial distribution of the small signal gain. The rich iodine condition produces some negative gain regions along the jet trajectory, while the lean iodine condition slows down the development of the gain in the streamwise direction. It is also found that the new configuration of an interleaving jet helps form a reasonable gain field under appropriate operation conditions. (c) 2007 Elsevier Ltd. All rights reserved.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.

Numerical study of sub-wavelength plasmonic waveguide

The authors present an analysis of a plasmonic waveguide, simulated using a two-dimensional finite-difference time-domain technique. With the surface structures located on the surface of the metal, the device is able to confine and guide light waves in a sub-wavelength scale. And two waveguides can be placed within 150 nm (similar to 6% of the incident wavelength) that will helpful for the optoelectronic integration. Within the 20 mu m simulation region, it is found that the intensity of the guided light at the interface is roughly two to four times the peak intensity of the incident light, and the propagation length can reach approximately 40 Pm at the wavelength of 2.44 mu m. (c) 2007 Elsevier B.V. All rights reserved.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.