In forest science and practice, the total tree height is one of the basic morphometric attributes at the tree level and it has been closely linked with important stand attributes. In the current research, sixteen nonl...In forest science and practice, the total tree height is one of the basic morphometric attributes at the tree level and it has been closely linked with important stand attributes. In the current research, sixteen nonlinear functions for height prediction were tested in terms of their fitting ability against samples of Abies borisii regis and Pinus sylvestris trees from mountainous forests in central Greece. The fitting procedure was based on generalized nonlinear weighted regression. At the final stage, a five-quantile nonlinear height-diameter model was developed for both species through a quantile regression approach, to estimate the entire conditional distribution of tree height, enabling the evaluation of the diameter impact at various quantiles and providing a comprehensive understanding of the proposed relationship across the distribution. The results clearly showed that employing the diameter as the sole independent variable, the 3-parameter Hossfeld function and the 2-parameter N?slund function managed to explain approximately 84.0% and 81.7% of the total height variance in the case of King Boris fir and Scots pine species, respectively. Furthermore, the models exhibited low levels of error in both cases(2.310m for the fir and 3.004m for the pine), yielding unbiased predictions for both fir(-0.002m) and pine(-0.004m). Notably, all the required assumptions for homogeneity and normality of the associated residuals were achieved through the weighting procedure, while the quantile regression approach provided additional insights into the height-diameter allometry of the specific species. The proposed models can turn into valuable tools for operational forest management planning, particularly for wood production and conservation of mountainous forest ecosystems.展开更多
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...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%.展开更多
In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws...In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.展开更多
In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded be...In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.展开更多
In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbol...In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.展开更多
A resolution method based on Gaussian-like distribution for overlapped linear sweep polarographic peaks was proposed to simultaneously detect the polymetallic components, such as Zn（Ⅱ） and Co（Ⅱ）, coexisting in t...A resolution method based on Gaussian-like distribution for overlapped linear sweep polarographic peaks was proposed to simultaneously detect the polymetallic components, such as Zn（Ⅱ） and Co（Ⅱ）, coexisting in the leaching solution of zinc hydrometallurgy. A Gaussian-like distribution was constructed as the sub-model of overlapped peaks by analyzing the characteristics of linear sweep polarographic curve. Then, the abscissas of each peak and trough were pinpointed through multi-resolution wavelet decomposition, the curve and its derivative curves were fitted by using nonlinear weighted least squares （NWLS）. Finally, overlapped peaks were resolved into independent sub-peaks based on fitted reconstruction parameters. The experimental results show that the relative error of half-wave potential pinpointed by multi-resolution wavelet decomposition is less than 1% and the accuracy of Ip fitted by NWLS is higher than 96%. The proposed resolution method is effective for overlapped linear sweep polarographic peaks of Zn（Ⅱ） and Co（Ⅱ）.展开更多
In this article,novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi eq...In this article,novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations.These novel smoothness indicators are constructed from the derivatives of reconstructed polynomials over each sub-stencil.The constructed smoothness indicators measure the arc-length of the reconstructed polynomials so that the new nonlinear weights could get less absolute truncation error and give a high-resolution numerical solution.Extensive numerical tests are conducted and presented to show the performance capability and the numerical accuracy of the proposed scheme with the comparison to the classical WENO scheme.展开更多
The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation e...The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares （WTLS） technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix （VCM） of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints （NWTLS-EC） for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality （LSE） constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.展开更多
The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes （WCNS） [Deng X. and Zhang H. （2000）, J. Comput. Phys. 165, 22–44 and Zhang S., Jiang S. and Shu C.-W. （2008...The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes （WCNS） [Deng X. and Zhang H. （2000）, J. Comput. Phys. 165, 22–44 and Zhang S., Jiang S. and Shu C.-W. （2008）, J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. （2007）, J. Sci. Comput. 31, 273–305 and Zhang S., Jiang S and Shu. C.-W. （2011）, J. Sci. Comput. 47, 216–238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.展开更多
This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nire...This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.展开更多
Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of el...Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.展开更多
In this paper,we introduce a new averaging rule,the nonlinear weighted averaging rule.As an application,this averaging rule is used to replace the midpoint averaging in the de Casteljau evaluation algorithm and with t...In this paper,we introduce a new averaging rule,the nonlinear weighted averaging rule.As an application,this averaging rule is used to replace the midpoint averaging in the de Casteljau evaluation algorithm and with this scheme we can also generate transcendental functions which cannot be generated by the classical de Casteljau algorithm.We also investigate the properties of the curves of the functions generated by blossoming,where the results show that these curves and the classical Bézier curves have some similar properties,including variation diminishing property and endpoint interpolation.However,the curves obtained by blossoming using nonlinear weighted averaging rules induced by certain functions violate some properties like convex hull property.展开更多
It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors.In this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water eq...It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors.In this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water equations in prebalanced forms.The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term.Some numerical examples in oneand two-dimensions are also presented to demonstrate the well-balanced property,high order accuracy and good shock capturing capability of the proposed scheme.展开更多
Since the classical weighted essentially non-oscillatory(WENO)scheme is proposed,various improved versions have been developed,and a typical one is the WENO-Z scheme.Although better resolution is achieved,it is shown ...Since the classical weighted essentially non-oscillatory(WENO)scheme is proposed,various improved versions have been developed,and a typical one is the WENO-Z scheme.Although better resolution is achieved,it is shown in this article that,the result of WENO-Z scheme suffers evident distortion in the long-time simulation of the linear advection equation.In order to fix the problem of WENO-Z,a symmetrypreserving mapping method is proposed in this article.In the original mapping method,the weight of each sub-stencil is used to map,which is demonstrated to cause asymmetric improvement about a discontinuity.This asymmetric improvement will lead to a distorted solution,more severe with longer output time.In the symmetry-preserving mapping method,a new variable related to the smoothness indicator is selected to map,which has the same ideal value for each sub-stencil.Using the new mapping method can not only fix the distortion problem of WENO-Z,but also improve the numerical resolution.Several benchmark problems are conducted to show the improved performance of the resultant scheme.展开更多
The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order differ...The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.展开更多
A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for ...A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.展开更多
This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variab...This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variables for the specific dissipation rate(o)are implemented in the framework of the Reynolds stress model(RSM)for improving its robustness.Specifically,g(=1/√ω)has natural boundary conditions and reduced spatial gradients,and a new numerical constraint is imposed on itω(=lnω)can preserve positivity and also has reduced spatial gradients;the eddy viscosity v,also has natural boundary conditions and its equation is improved in this work.The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme(WCNS).Moreover,several numerical techniques are introduced to improve the numerical stability of the equation system.A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models.Numerical results show that the scale-transformed models have significantly improved robustness compared to the w model and still keep the characteristics of RSM.Therefore,the high-order discretization of the RANS and RSM equations,which number 12 in total,can be successfully achieved.展开更多
文摘In forest science and practice, the total tree height is one of the basic morphometric attributes at the tree level and it has been closely linked with important stand attributes. In the current research, sixteen nonlinear functions for height prediction were tested in terms of their fitting ability against samples of Abies borisii regis and Pinus sylvestris trees from mountainous forests in central Greece. The fitting procedure was based on generalized nonlinear weighted regression. At the final stage, a five-quantile nonlinear height-diameter model was developed for both species through a quantile regression approach, to estimate the entire conditional distribution of tree height, enabling the evaluation of the diameter impact at various quantiles and providing a comprehensive understanding of the proposed relationship across the distribution. The results clearly showed that employing the diameter as the sole independent variable, the 3-parameter Hossfeld function and the 2-parameter N?slund function managed to explain approximately 84.0% and 81.7% of the total height variance in the case of King Boris fir and Scots pine species, respectively. Furthermore, the models exhibited low levels of error in both cases(2.310m for the fir and 3.004m for the pine), yielding unbiased predictions for both fir(-0.002m) and pine(-0.004m). Notably, all the required assumptions for homogeneity and normality of the associated residuals were achieved through the weighting procedure, while the quantile regression approach provided additional insights into the height-diameter allometry of the specific species. The proposed models can turn into valuable tools for operational forest management planning, particularly for wood production and conservation of mountainous forest ecosystems.
基金Project supported by the National Key Project(No.GJXM92579)the Defense Industrial Technology Development Program(No.C1520110002)the State Administration of Science,Technology and Industry for National Defence,China。
文摘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%.
基金Project supported by the National Natural Science Foundation of China(No.11571366)the Basic Research Foundation of National Numerical Wind Tunnel Project(No.NNW2018-ZT4A08)
文摘In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.
文摘In this paper, we consider gradient estimates for positive solutions to the following weighted nonlinear parabolic equations on a complete smooth metric measure space with only Bakry-Émery Ricci tensor bounded below: One is $${u_t} = {\Delta _f}u + au\log u + bu$$ with a, b two real constants, and another is $${u_t} = {\Delta _f}u + \lambda {u^\alpha }$$ with λ, α two real constants. We obtain local Hamilton-Souplet-Zhang type gradient estimates for the above two nonlinear parabolic equations. In particular, our estimates do not depend on any assumption on f.
基金the NSFC grant 11872210 and the Science Challenge Project,No.TZ2016002the NSFC Grant 11926103 when he visited Tianyuan Mathematical Center in Southeast China,Xiamen 361005,Fujian,Chinathe NSFC Grant 12071392 and the Science Challenge Project,No.TZ2016002.
文摘In this paper,a new type of finite difference mapped weighted essentially non-oscillatory(MWENO)schemes with unequal-sized stencils,such as the seventh-order and ninthorder versions,is constructed for solving hyperbolic conservation laws.For the purpose of designing increasingly high-order finite difference WENO schemes,the equal-sized stencils are becoming more and more wider.The more we use wider candidate stencils,the bigger the probability of discontinuities lies in all stencils.Therefore,one innovation of these new WENO schemes is to introduce a new splitting stencil methodology to divide some fourpoint or five-point stencils into several smaller three-point stencils.By the usage of this new methodology in high-order spatial reconstruction procedure,we get different degree polynomials defined on these unequal-sized stencils,and calculate the linear weights,smoothness indicators,and nonlinear weights as specified in Jiang and Shu(J.Comput.Phys.126:202228,1996).Since the difference between the nonlinear weights and the linear weights is too big to keep the optimal order of accuracy in smooth regions,another crucial innovation is to present the new mapping functions which are used to obtain the mapped nonlinear weights and decrease the difference quantity between the mapped nonlinear weights and the linear weights,so as to keep the optimal order of accuracy in smooth regions.These new MWENO schemes can also be applied to compute some extreme examples,such as the double rarefaction wave problem,the Sedov blast wave problem,and the Leblanc problem with a normal CFL number.Extensive numerical results are provided to illustrate the good performance of the new finite difference MWENO schemes.
基金Project(2012BAF03B05)supported by the National Key Technology R&D Program of ChinaProject(61025015)supported by the National Natural Science Foundation for Distinguished Young Scholars of China+1 种基金Project(61273185)supported by the National Natural Science Foundation of ChinaProject(2012CK4018)supported by the Science and Technology Project of Hunan Province,China
文摘A resolution method based on Gaussian-like distribution for overlapped linear sweep polarographic peaks was proposed to simultaneously detect the polymetallic components, such as Zn（Ⅱ） and Co（Ⅱ）, coexisting in the leaching solution of zinc hydrometallurgy. A Gaussian-like distribution was constructed as the sub-model of overlapped peaks by analyzing the characteristics of linear sweep polarographic curve. Then, the abscissas of each peak and trough were pinpointed through multi-resolution wavelet decomposition, the curve and its derivative curves were fitted by using nonlinear weighted least squares （NWLS）. Finally, overlapped peaks were resolved into independent sub-peaks based on fitted reconstruction parameters. The experimental results show that the relative error of half-wave potential pinpointed by multi-resolution wavelet decomposition is less than 1% and the accuracy of Ip fitted by NWLS is higher than 96%. The proposed resolution method is effective for overlapped linear sweep polarographic peaks of Zn（Ⅱ） and Co（Ⅱ）.
文摘In this article,novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of Hamilton-Jacobi equations.These novel smoothness indicators are constructed from the derivatives of reconstructed polynomials over each sub-stencil.The constructed smoothness indicators measure the arc-length of the reconstructed polynomials so that the new nonlinear weights could get less absolute truncation error and give a high-resolution numerical solution.Extensive numerical tests are conducted and presented to show the performance capability and the numerical accuracy of the proposed scheme with the comparison to the classical WENO scheme.
基金supported by the National Natural Science Foundation of China(41074017)
文摘The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares （WTLS） technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix （VCM） of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints （NWTLS-EC） for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality （LSE） constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.
基金Supported by the National Natural Science Foundation of China(Grants11172317,91016001)973 Program 2009CB724104,Supported by 973 program 2009CB723800+1 种基金Supported by AFOSR Grant FA9550-09-1-0126NSF grants DMS-0809086 and DMS-1112700
文摘The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes （WCNS） [Deng X. and Zhang H. （2000）, J. Comput. Phys. 165, 22–44 and Zhang S., Jiang S. and Shu C.-W. （2008）, J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. （2007）, J. Sci. Comput. 31, 273–305 and Zhang S., Jiang S and Shu. C.-W. （2011）, J. Sci. Comput. 47, 216–238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.
文摘This paper deals with the existence and multiplicity of nontrivial solutions to a weighted nonlinear elliptic system with nonlinear homogeneous boundary condition in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and variational method, we prove that the system has at least two nontrivial solutions when the parameter λ belongs to a certain subset of R.
文摘Conventional attractive magnetic force models (proportional to the coil current squared and inversely proportional to the gap squared) cannot simulate the nonlinear responses of magnetic bearings in the presence of electromagnetic losses,flux leakage or saturation of iron.In this paper,based on results from an experimental set-up designed to study magnetic force,a novel parametric model is presented in the form of a nonlinear polynomial with unknown coefficients.The parameters of the proposed model are identified using the weighted residual method.Validations of the model identified were performed by comparing the results in time and frequency domains.The results show a good correlation between experiments and numerical simulations.
文摘In this paper,we introduce a new averaging rule,the nonlinear weighted averaging rule.As an application,this averaging rule is used to replace the midpoint averaging in the de Casteljau evaluation algorithm and with this scheme we can also generate transcendental functions which cannot be generated by the classical de Casteljau algorithm.We also investigate the properties of the curves of the functions generated by blossoming,where the results show that these curves and the classical Bézier curves have some similar properties,including variation diminishing property and endpoint interpolation.However,the curves obtained by blossoming using nonlinear weighted averaging rules induced by certain functions violate some properties like convex hull property.
基金The work is supported by the Basic Research Foundation of the National NumericalWind Tunnel Project(Grant No.NNW2018-ZT4A08)the National Natural Science Foundation(Grant No.11972370)the National Key Project(Grant No.GJXM92579)of China.
文摘It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors.In this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water equations in prebalanced forms.The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term.Some numerical examples in oneand two-dimensions are also presented to demonstrate the well-balanced property,high order accuracy and good shock capturing capability of the proposed scheme.
基金National Natural Science Foundation of China(No.11732013)National Numerical Windtunnel(No.NNW2019ZT3-A15)Foundation of National Key Laboratory(No.JCKYS6142201190304).
文摘Since the classical weighted essentially non-oscillatory(WENO)scheme is proposed,various improved versions have been developed,and a typical one is the WENO-Z scheme.Although better resolution is achieved,it is shown in this article that,the result of WENO-Z scheme suffers evident distortion in the long-time simulation of the linear advection equation.In order to fix the problem of WENO-Z,a symmetrypreserving mapping method is proposed in this article.In the original mapping method,the weight of each sub-stencil is used to map,which is demonstrated to cause asymmetric improvement about a discontinuity.This asymmetric improvement will lead to a distorted solution,more severe with longer output time.In the symmetry-preserving mapping method,a new variable related to the smoothness indicator is selected to map,which has the same ideal value for each sub-stencil.Using the new mapping method can not only fix the distortion problem of WENO-Z,but also improve the numerical resolution.Several benchmark problems are conducted to show the improved performance of the resultant scheme.
基金Foundation items： National Basic Research Program of China （2009CB723801） National Natural Science Foundation of China （11072259）
文摘The Spalart-Allmaras （S-A） turbulence model, the shear-stress transport （SST） turbulence model and their compressibility corrections are revaluated for hypersonic compression comer flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme （WCNS-E-5） is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression comers at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris＇ and Shur＇s compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris＇ modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.
基金Supported by National Natural Science Foundation of China(40974065, 41025015)Scientific and Technological Innovative Team in Sichuan Province(2011JTD0013)"863" Program of China(2012AA063501)
文摘A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.
基金supported by the National Natural Science Foundation of China(Grant No.12002379)the Natural Science Foundation of Hunan Province in China(Grant No.2020JJ5648)+1 种基金the Scientific Research Project of National University of Defense Technology(Grant No.ZK20-43)the National Key Project(Grant No.GJXM92579).
文摘This paper is set in the high-order finite-difference discretization of the Reynolds-averaged Navier-Stokes(RANS)equations,which are coupled with the turbulence model equations.Three alternative scale-providing variables for the specific dissipation rate(o)are implemented in the framework of the Reynolds stress model(RSM)for improving its robustness.Specifically,g(=1/√ω)has natural boundary conditions and reduced spatial gradients,and a new numerical constraint is imposed on itω(=lnω)can preserve positivity and also has reduced spatial gradients;the eddy viscosity v,also has natural boundary conditions and its equation is improved in this work.The solution polynomials of the mean-flow and turbulence-model equations are both reconstructed by the weighted compact nonlinear scheme(WCNS).Moreover,several numerical techniques are introduced to improve the numerical stability of the equation system.A range of canonical as well as industrial turbulent flows are simulated to assess the accuracy and robustness of the scale-transformed models.Numerical results show that the scale-transformed models have significantly improved robustness compared to the w model and still keep the characteristics of RSM.Therefore,the high-order discretization of the RANS and RSM equations,which number 12 in total,can be successfully achieved.
