COMPACT FINITE DIFFERENCE-FOURIER SPECTRAL METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Soil and Vegetation Spectral Coupling Difference (SVSCD) for Minerals Extraction from Hyperion Data in Vegetation Covered Area

Remote sensing data have been widely applied to extract minerals in geologic exploration, however, in areas covered by vegetation, extracted mineral information has mostly been small targets bearing little information. In this paper, we present a new method for mineral extraction aimed at solving the difficulty of mineral identification in vegetation covered areas. The method selected six sets of spectral difference coupling between soil and plant(SVSCD). These sets have the same vegetation spectra reflectance and a maximum different reflectance of soil and mineral spectra from Hyperion image based on spectral reflectance characteristics of measured spectra. The central wavelengths of the six, selected band pairs were 2314 and 701 nm, 1699 and 721 nm, 1336 and 742 nm, 2203 and 681 nm, 2183 and 671 nm, and 2072 and 548 nm. Each data set's reflectance was used to calculate the difference value. After band difference calculation, vegetation information was suppressed and mineral abnormal information was enhanced compared to the scatter plot of original band. Six spectral difference couplings, after vegetation inhibition, were arranged in a new data set that requires two components that have the largest eigenvalue difference from principal component analysis(PCA). The spatial geometric structure features of PC1 and PC2 was used to identify altered minerals by spectral feature fitting(SFF). The collecting rocks from the 10 points that were selected in the concentration of mineral extraction were analyzed under a high-resolution microscope to identify metal minerals and nonmetallic minerals. Results indicated that the extracted minerals were well matched with the verified samples, especially with the sample 2, 4, 5 and 8. It demonstrated that the method can effectively detect altered minerals in vegetation covered area in Hyperion image.

Simple method for extracting the seasonal signals of photochemical reflectance index and normalized difference vegetation index measured using a spectral reflectance sensor

A spectral reflectance sensor(SRS)fixed on the near-surface ground was developed to support the continuous monitoring of vegetation indices such as the normalized difference vegetation index(NDVI)and photochemical reflectance index(PRI).NDVI is useful for indicating crop growth/phenology,whereas PRI was developed for observing physiological conditions.Thus,the seasonal change patterns of NDVI and PRI are two valuable pieces of information in a crop-monitoring system.However,capturing the seasonal patterns is considered challenging because the vegetation index values estimated by the reflection from vegetation are often governed by meteorological conditions,such as solar irradiance and precipitation.Further,unlike growth/phenology,the physiological condition has diurnal changes as well as seasonal characteristics.This study proposed a novel filtering method for extracting the seasonal signals of SRS-based NDVI and PRI in paddy rice,barley,and garlic.First,the measurement accuracy of SRSs was compared with handheld spectrometers,and the R^(2)values between the two devices were 0.96 and 0.81 for NDVI and PRI,respectively.Second,the experimental study of threshold criteria with respect to meteorological variables(i.e.,insolation,cloudiness,sunshine duration,and precipitation)was conducted,and sunshine duration was the most useful one for excluding distorted values of the vegetation indices.After data processing based on sunshine duration,the R^(2)values between the measured vegetation indices and the extracted seasonal signals of vegetation indices increased by approximately 0.002–0.004(NDVI)and 0.065–0.298(PRI)on the three crops,and the seasonal signals of vegetation indices became noticeably improved.This method will contribute to an agricultural monitoring system by identifying the seasonal changes in crop growth and physiological conditions.

Finite Difference Preconditioners for Legendre Based Spectral Element Methods on Elliptic Boundary Value Problems

Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.

Comparison of finite difference and pseudo-spectral methods in forward modelling based on metal ore model of random media

With more applications of seismic exploration in metal ore exploration,forward modelling of seismic wave has become more important in metal ore. Finite difference method and pseudo-spectral method are two important methods of wave-field simulation. Results of previous studies show that both methods have distinct advantages and disadvantages: Finite difference method has high precision but its dispersion is serious; pseudospectral method considers both computational efficiency and precision but has less precision than finite-difference. The authors consider the complex structural characteristics of the metal ore,furthermore add random media in order to simulate the complex effects produced by metal ore for wave field. First,the study introduced the theories of random media and two forward modelling methods. Second,it compared the simulation results of two methods on fault model. Then the authors established a complex metal ore model,added random media and compared computational efficiency and precision. As a result,it is found that finite difference method is better than pseudo-spectral method in precision and boundary treatment,but the computational efficiency of pseudospectral method is slightly higher than the finite difference method.

A Spectral Finite Difference Method for Analysis of a Fluid-Lubricated Herringbone Grooves Journal Bearing under a Special Case at Rectangle Groove

A spectral difference method is applied to get numerical solutions for a fluid-lubricated herringbone grooved journal bearing with trapezoidal grooves by previous work of the authors. However, an inexpedience in which Fourier series of the film profile does not converge at jump points of groove start or groove end in the case of rectangle groove was still remained. In the paper, an inexpedience of numerical analysis under a special case at rectangle groove is challenged to solve. As a result, for compensation of which Fourier series does not converge at jump points in a special case of rectangle groove, Fourier coefficient of fluid film thickness is proposed as taking the limit of which in a case trapezoidal groove at trapezoidal angle approaches 0.

Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic

A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the computation costs,the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations.The effectiveness of the proposed algorithm is verified by the first numerical example.The mass conservation property and stability statement are confirmed by two other numerical examples.

ERROR ESTIMATION OF SPECTRAL-DIFFERENCE METHOD FOR COMPRESSIBLE FLUID FLOW IN THREE-DIMENSIONAL SPACE

This paper is devoted to a combined Fourier spectral-finite difference method for solving 3-dimensional, semi-periodic compressible fluid flow problem. The error estimation, as well as the convergence rate, is presented.

One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary

Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.

New optimized flux difference schemes for improving high-order weighted compact nonlinear scheme with applications

To improve the spectral characteristics of the high-order weighted compact nonlinear scheme(WCNS),optimized flux difference schemes are proposed.The disadvantages in previous optimization routines,i.e.,reducing formal orders,or extending stencil widths,are avoided in the new optimized schemes by utilizing fluxes from both cell-edges and cell-nodes.Optimizations are implemented with Fourier analysis for linear schemes and the approximate dispersion relation(ADR)for nonlinear schemes.Classical difference schemes are restored near discontinuities to suppress numerical oscillations with use of a shock sensor based on smoothness indicators.The results of several benchmark numerical tests indicate that the new optimized difference schemes outperform the classical schemes,in terms of accuracy and resolution for smooth wave and vortex,especially for long-time simulations.Using optimized schemes increases the total CPU time by less than 4%.

HARTEN SOLUTION FOR ONE-DIMENSIONAL UNSTEADY EQUATION

In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations of the direct reflection of the strong plane detonation wave meeting a solid wall barrier,in this paper,we technically construct the difference schemes of the boundary and sub-boundary of the problem,and deduce the auto-analogue analytic solutions of the initial value problem,and at the same time,we present a method for the singular property of the initial value problem,from which we can get a satisfactory computation result of this difficult problem.The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth generalization.

Porosity Evaluation and the Power Spectral Densities Analyses of Carbon-Nickel Composite Films Annealed at Different Temperatures

The densification and the fractal dimensions of carbon-nickel films annealed at different temperatures 300, 500, 800, and 1000℃ with emphasis on porosity evaluation are investigated. For this purpose, the refractive index of films is determined from transmittance spectra. Three different regimes are identified, T 〈 500℃, 500℃ 〈 T 〈 800℃ and T 〉 800℃. The Rutherford baekscattering spectra show that with increasing the annealing temperature, the concentration of nickel atoms into films decreases. It is shown that the effect of annealing temperatures for increasing films densification at T 〈 500℃ and T 〉 800℃ is greater than the effect of nickel concentrations. It is observed that the effect of decreasing nickel atoms into films at 500℃ 〈 T 〈 800℃ strongly causes improving porosity and decreasing densification. The fractal dimensions of carbon-nickel films annealed from 300 to 500℃ are increased, while from 500 to 1000℃ these characteristics are decreased. It can be seen that at 800℃, films have maximum values of porosity and roughness.

Alternating Group Explicit Iterative Methods for One-Dimensional Advection-Diffusion Equation

The finite difference method such as alternating group iterative methods is useful in numerical method for evolutionary equations and this is the standard approach taken in this paper. Alternating group explicit (AGE) iterative methods for one-dimensional convection diffusion equations problems are given. The stability and convergence are analyzed by the linear method. Numerical results of the model problem are taken. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show that the behavior of the method with emphasis on treatment of boundary conditions is valuable.

THE DYNAMICAL BEHAVIOR OF FULLY DISCRETE SPECTRAL METHOD FOR NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to

Lithological mapping with multispectral data–setup and application of a spectral database for rocks in the Balakot area, Northern Pakistan

In the frame of landslide susceptibility assessment, a spectral library was created to support the identification of materials confined to a particular region using remote sensing images. This library, called Pakistan spectral library(pklib) version 0.1, contains the analysis data of sixty rock samples taken in the Balakot region in Northern Pakistan.The spectral library is implemented as SQLite database. Structure and naming are inspired by the convention system of the ASTER Spectral Library. Usability, application and benefit of the pklib were evaluated and depicted taking two approaches, the multivariate and the spectral based. The spectral information were used to create indices. The indices were applied to Landsat and ASTER data tosupportthespatial delineation of outcropping rock sequences instratigraphic formations. The application of the indices introduced in this paper helps to identify spots where specific lithological characteristics occur. Especially in areas with sparse or missing detailed geological mapping, the spectral discrimination via remote sensing data can speed up the survey. The library can be used not only to support the improvement of factor maps for landslide susceptibility analysis, but also to provide a geoscientific basisto further analyze the lithological spotin numerous regions in the Hindu Kush.

Chebyshev Pseudo-Spectral Method for Solving Fractional Advection-Dispersion Equation

Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional Advection-dispersion equation (ADE) is considered. The fractional derivative is described in the Caputo sense. The method is based on Chebyshev approximations. The properties of Chebyshev polynomials are used to reduce ADE to a system of ordinary differential equations, which are solved using the finite difference method (FDM). Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. Numerical solutions of ADE are presented and the results are compared with the exact solution.

Estimation of rock Fe content based on hyperspectral indices

Information on the Fe content of bare rocks is needed for implementing geochemical processes and identifying mines.However,the influence of Fe content on the spectra of bare rocks has not been thoroughly analyzed in previous studies.The Saur Mountain region within the Hoboksar of the Russell Hill depression was selected as the study area.Specifically,we analyzed six hyperspectral indices related to rock Fe content based on laboratory measurements(Dataset I)and field measurements(Dataset II).In situ field measurements were acquired to verify the laboratory measurements.Fe content of the rock samples collected from different fresh and weathered rock surfaces were divided into six levels to reveal the spatial distributions of Fe content of these samples.In addition,we clearly displayed wavelengths with obvious characteristics by analyzing the spectra of these samples.The results of this work indicated that Fe content estimation models based on the fresh rock surface measurements in the laboratory can be applied to in situ field or satellite-based measurements of Fe content of the weathered rock surfaces.It is not the best way to use only the single wavelengths reflectance at all absorption wavelengths or the depth of these absorption features to estimate Fe content.Based on sample data analysis,the comparison with other indices revealed that the performance of the modified normalized difference index is the best indicator for estimating rock Fe content,with R2 values of 0.45 and 0.40 corresponding to datasets I and II,respectively.Hence,the modified normalized difference index(the wavelengths of 2220,2290,and 2370 nm)identified in this study could contribute considerably to improve the identification accuracy of rock Fe content in the bare rock areas.The method proposed in this study can obviously provide an efficient solution for large-scale rock Fe content measurements in the field.

A Spectral Method for Convection-Diffusion Equations

In the practical problems such as nuclear waste pollution and seawater intrusion etc., many problems are reduced to solving the convection-diffusion equation, so the research of convection-diffusion equation is of great value. In this work, a spectral method is presented for solving one and two dimensional convection-diffusion equation with source term. The finite difference method is also used to solve the convection diffusion equation. The numerical experiments show that the spectral method is more efficient than other methods for solving the convection-diffusion equation.

Calogero Model with Different Masses

We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Here, we factorize the ground stateout of the Hamiltonian H in order to get the new operatorwhich preserves some spaces of polynomialsin the case of equal masses, i.e. (the usual Calogero model) and in the case with different masses. The spectrum of these both cases is found easily.

VTI介质修正声学近似qP波波动方程与模拟

各向异性介质中纵横波通常耦合在一起传播,纵横波解耦是地震波传播理论研究的重要内容。经典的声学近似通过设置垂向qSV波速度V_(S0)为0来解耦qP波场,但是存在退化qSV波等问题。本研究将垂向qSV波速度V_(S0)考虑成波数k_(x)、k_(z)和各向异性参数ε、δ的函数,对声学近似进行修正,推导了VTI介质修正声学近似qP波频散关系和波动方程。VTI介质修正声学近似qP波波动方程包含椭圆项和非椭圆项两部分,因此采用混合有限差分/伪谱算法进行求解,即采用有限差分法求解椭圆项、伪谱法求解非椭圆项。频散关系分析和数值示例表明,基于修正声学近似的qP波波动方程不包含退化qSV波,是纯qP波方程,与弹性波方程模拟结果吻合较好,且具有较高精度;该方程在ε≥δ和ε<δ的VTI介质中均是稳定的,并且精度高于声学近似模拟结果。