In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the m...In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the main contributor to the stability of the slope.Then,two widening schemes are proposed,which are the steep slope with strong support and the gentle slope with general support schemes.The static/slope module of MIDAS GTS finite element analysis software and the strength reduction method were used to compare the two schemes.The results show that the steep slope with a strong support scheme has obvious advantages in land requisition,environmental protection,and safety and is more suitable for reconstructing and expanding the highway slope.展开更多
We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH nume...We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.展开更多
In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the targe...In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.展开更多
Sediment transport can be modelled using hydrodynamic models based on shallow water equations coupled with the sediment concentration conservation equation and the bed con-servation equation.The complete system of equ...Sediment transport can be modelled using hydrodynamic models based on shallow water equations coupled with the sediment concentration conservation equation and the bed con-servation equation.The complete system of equations is made up of the energy balance law and the Exner equations.The numerical solution for this complete system is done in a seg-regated manner.First,the hyperbolic part of the system of balance laws is solved using a finite volume scheme.Three ways to compute the numerical flux have been considered,the Q-scheme of van Leer,the HLLCS approximate Riemann solver,and the last one takes into account the presence of non-conservative products in the model.The discretisation of the source terms is carried out according to the numerical flux chosen.In the second stage,the bed conservation equation is solved by using the approximation computed for the system of balance laws.The numerical schemes have been validated making comparisons between the obtained numerical results and the experimental data for some physical experiments.The numerical results show a good agreement with the experimental data.展开更多
In Mobile Communication Systems, inter-cell interference becomes one of the challenges that degrade the system’s performance, especially in the region with massive mobile users. The linear precoding schemes were prop...In Mobile Communication Systems, inter-cell interference becomes one of the challenges that degrade the system’s performance, especially in the region with massive mobile users. The linear precoding schemes were proposed to mitigate interferences between the base stations (inter-cell). These schemes are categorized into linear and non-linear;this study focused on linear precoding schemes, which are grounded into three types, namely Zero Forcing (ZF), Block Diagonalization (BD), and Signal Leakage Noise Ratio (SLNR). The study included the Cooperative Multi-cell Multi Input Multi Output (MIMO) System, whereby each Base Station serves more than one mobile station and all Base Stations on the system are assisted by each other by shared the Channel State Information (CSI). Based on the Multi-Cell Multiuser MIMO system, each Base Station on the cell is intended to maximize the data transmission rate by its mobile users by increasing the Signal Interference to Noise Ratio after the interference has been mitigated due to the usefully of linear precoding schemes on the transmitter. Moreover, these schemes used different approaches to mitigate interference. This study mainly concentrates on evaluating the performance of these schemes through the channel distribution models such as Ray-leigh and Rician included in the presence of noise errors. The results show that the SLNR scheme outperforms ZF and BD schemes overall scenario. This implied that when the value of SNR increased the performance of SLNR increased by 21.4% and 45.7% for ZF and BD respectively.展开更多
Due to the anonymity of blockchain,frequent security incidents and attacks occur through it,among which the Ponzi scheme smart contract is a classic type of fraud resulting in huge economic losses.Machine learningbase...Due to the anonymity of blockchain,frequent security incidents and attacks occur through it,among which the Ponzi scheme smart contract is a classic type of fraud resulting in huge economic losses.Machine learningbased methods are believed to be promising for detecting ethereum Ponzi schemes.However,there are still some flaws in current research,e.g.,insufficient feature extraction of Ponzi scheme smart contracts,without considering class imbalance.In addition,there is room for improvement in detection precision.Aiming at the above problems,this paper proposes an ethereum Ponzi scheme detection scheme through opcode context analysis and adaptive boosting(AdaBoost)algorithm.Firstly,this paper uses the n-gram algorithm to extract more comprehensive contract opcode features and combine them with contract account features,which helps to improve the feature extraction effect.Meanwhile,adaptive synthetic sampling(ADASYN)is introduced to deal with class imbalanced data,and integrated with the Adaboost classifier.Finally,this paper uses the improved AdaBoost classifier for the identification of Ponzi scheme contracts.Experimentally,this paper tests our model in real-world smart contracts and compares it with representative methods in the aspect of F1-score and precision.Moreover,this article compares and discusses the state of art methods with our method in four aspects:data acquisition,data preprocessing,feature extraction,and classifier design.Both experiment and discussion validate the effectiveness of our model.展开更多
We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gor...We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.展开更多
There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity sch...There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity scheme(IVD scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall(MPB-C scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes(MPB-W scheme)and the geometric formulation scheme(GF scheme).But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past.In this paper,the numerical stability and accuracy of these schemes are clarified for the first time,by applying the five widely used contact angle schemes to simulate a two-dimensional(2D)sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively.(i)It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle,but the simulated contact angles by the PB scheme,IVD scheme,MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength.The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios.(ii)Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes,the magnitude of the spurious velocity in the PB scheme,IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme.(iii)The fluid density variation near the wall in the PB scheme is the most significant,and the variation can be diminished in the IVD scheme,MPB-C scheme andMPBWscheme.The variation totally disappeared in the GF scheme.(iv)For the simulation of capillary imbibition,the MPB-C scheme,MPB-Wscheme and GF scheme simulate the dynamics of the liquid-vapor interface well,with the GF scheme being the most accurate.The accuracy of the IVD scheme is low at a small contact angle(44 degrees)but gets high at a large contact angle(60 degrees).However,the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface.As a whole,it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting,while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.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
In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two ...In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two nonlinear schemes and two linearized schemes are presented. All resulting schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities are used to highlight the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be also conducted. The numerical results show that the interaction behavior is elastic and the conserved quantities are conserved exactly, and this is a good indication of the reliability of the schemes which we derived. A comparison with some existing is presented as well.展开更多
By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presentedin this paper by using suitable weights instead of the minmod funct...By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presentedin this paper by using suitable weights instead of the minmod functions appearingin various TVD schemes. Numerical comparisons between the weighted schemes andthe non-weighted schemes have been done for scalar equation, one-dimensional Eulerequations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokesequations.展开更多
The formation and development of typhoons are closely related to the disturbed low vortexes at the planetary boundary layer(PBL). The effects of five PBL parameterization schemes(PBL schemes hereinafter) on the trajec...The formation and development of typhoons are closely related to the disturbed low vortexes at the planetary boundary layer(PBL). The effects of five PBL parameterization schemes(PBL schemes hereinafter) on the trajectory,intensity, and distribution of physical quantities are studied using the mesoscale WRF model on Super Typhoon Sanba(2012) during its initial stage. Results show that the five PBL schemes exhibit significant different effects on the simulated intensity and path. The results simulated by QNSE and ACM2 without the Bogus method are close to the best track data in the numerical experiments. When the Bogus method is adopted, the simulated trajectories improve significantly because the initial field is close to the true data. Among the five PBL schemes, QNSE and ACM2 with the Bogus method present improved simulated path and intensity compared with the three other schemes. This finding indicates that the two schemes deal with the initial PBL process satisfactorily, especially in the formation and development of disturbed low vortexes. The differences in the treatment methods of the five PBL schemes affect the surface layer physical quantities and the middle and upper atmospheres during the middle to late periods of the typhoon.Although QNSE and ACM2 present better simulation results than other schemes, they exhibit a few differences in the internal structure of the typhoon. The results simulated by MYJ are worse, and this method may be unsuitable for studying the formation and development of typhoons.展开更多
This paper evaluates the skills of physical Parameterization schemes in simulating extreme rainfall events over Dar es Salaam Region, Tanzania using the Weather Research and Forecasting (WRF) model. The model skill is...This paper evaluates the skills of physical Parameterization schemes in simulating extreme rainfall events over Dar es Salaam Region, Tanzania using the Weather Research and Forecasting (WRF) model. The model skill is determined during the 21 December 2011 flooding event. Ten sensitivity experiments have been conducted using Cumulus, Convective and Planetary boundary layer schemes to find the best combination and optimize the WRF model for the study area for heavy rainfall events. Model simulation results were verified against observed data using standard statistical tests. The model simulations show encouraging and better statistical results with the combination of Kain-Fritsch cumulus parameterization scheme, Lin microphysics scheme and Asymmetric Convection Model 2 (ACM2) planetary boundary scheme than any other combinations of physical parameterization schemes over Dar es Salaam region.展开更多
In this paper, we present a study of thermal, average power scaling, change in index of refraction and stress in photonic crystal fiber lasers with different pump schemes: forward pump scheme, backward pump scheme, fo...In this paper, we present a study of thermal, average power scaling, change in index of refraction and stress in photonic crystal fiber lasers with different pump schemes: forward pump scheme, backward pump scheme, forward pump scheme with reflection of 98%, backward pump scheme with reflection of 98% and bi-directional pump scheme. We show that management of thermal effects in fiber lasers will determine the efficiency and success of scaling-up efforts. In addition, we show that the most suitable scheme is the bi-directional.展开更多
The mei-yu front heavy rainstorms occurred over Nanjing on 3 5 and 8 9 July 2003 and were simulated in this paper using the Weather Research and Forecasting Model (WRFv3.1) with various mesoscale convection parameteri...The mei-yu front heavy rainstorms occurred over Nanjing on 3 5 and 8 9 July 2003 and were simulated in this paper using the Weather Research and Forecasting Model (WRFv3.1) with various mesoscale convection parameterization schemes (MCPSs). The simulations show that the temporal and spatial evolution and distribution of rainstorms can be modeled; however, there was incongruity between the comparative simulations of four different MCPSs and the observed data. These disparities were exhibited in the simulations of both the 24-hour surface rainfall total and the hourly precipitation rate. Further analysis revealed that the discrepancies of vertical velocity and the convective vorticity vector (CVV) between the four simulations were attributed to the deviation of rainfall values. In addition, the simulations show that the mid-scale convection, particularly the mesoscale convection system (MCS) formation, can be well simulated with the proper mesoscale convection parameterization schemes and may be a crucial factor of the mei-yu front heavy rainstorm. These results suggest that, in an effort to enhance simulation and prediction of heavy rainfall and rainstorms, subsequent studies should focus on the development and improvement of MCPS.展开更多
In order to investigate parameters of FAE (fuel air explosive) explosion, the two_phase gas_droplet conservation equations with two_dimensional axial symmetry in the Euler coordinate were used. High_resolution implici...In order to investigate parameters of FAE (fuel air explosive) explosion, the two_phase gas_droplet conservation equations with two_dimensional axial symmetry in the Euler coordinate were used. High_resolution implicit TVD (total variation diminishing) schemes were applied to gas phase equations and MacCormack schemes to liquid equations. The for mation and propagation of gas_droplet detonation wave were simulated numerically. The simulation results and the others are compared with a good agreement.展开更多
Various control schemes of automobile pollution are comprehensively evaluated by using the weighting and feyzzy methods, from which several feasible schemes are selected, and then mulit-target decision is made by usin...Various control schemes of automobile pollution are comprehensively evaluated by using the weighting and feyzzy methods, from which several feasible schemes are selected, and then mulit-target decision is made by using the minimum distance and hierarcby analysis methods, for determining the optimal control methods of automobile pollution.展开更多
Two kinds of symplectic schemes are proposed for the equations of vortex system in half plane.One is the Reflecting-method which is based on the symplectic schemes for the system in the whole plane.The other is constr...Two kinds of symplectic schemes are proposed for the equations of vortex system in half plane.One is the Reflecting-method which is based on the symplectic schemes for the system in the whole plane.The other is constructed directly according to the feature of the system.Aseries of numerical results are presented to show the effectiveness of our schemes.展开更多
文摘In this paper,the geological condition of the right-side slope of the K114+694–K115+162 section of Yong-tai-wen Expressway is investigated and analyzed with the results showing that the strength of rock mass is the main contributor to the stability of the slope.Then,two widening schemes are proposed,which are the steep slope with strong support and the gentle slope with general support schemes.The static/slope module of MIDAS GTS finite element analysis software and the strength reduction method were used to compare the two schemes.The results show that the steep slope with a strong support scheme has obvious advantages in land requisition,environmental protection,and safety and is more suitable for reconstructing and expanding the highway slope.
基金The work of B.S.Wang and W.S.Don was partially supported by the Ocean University of China through grant 201712011The work of A.Kurganov was supported in part by NSFC grants 11771201 and 1201101343by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘We construct new fifth-order alternative WENO(A-WENO)schemes for the Euler equations of gas dynamics.The new scheme is based on a new adaptive diffusion centralupwind Rankine-Hugoniot(CURH)numerical flux.The CURH numerical fluxes have been recently proposed in[Garg et al.J Comput Phys 428,2021]in the context of secondorder semi-discrete finite-volume methods.The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux,which was also developed with the help of the discrete RankineHugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in[Wang et al.SIAM J Sci Comput 42,2020].As in that work,we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes.The resulting one-and two-dimensional schemes are tested on a number of numerical examples,which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.
基金AFOSR and NSF for their support of this work under grants FA9550-19-1-0281 and FA9550-17-1-0394 and NSF grant DMS 191218。
文摘In this paper,we present a semi-Lagrangian(SL)method based on a non-polynomial function space for solving the Vlasov equation.We fnd that a non-polynomial function based scheme is suitable to the specifcs of the target problems.To address issues that arise in phase space models of plasma problems,we develop a weighted essentially non-oscillatory(WENO)scheme using trigonometric polynomials.In particular,the non-polynomial WENO method is able to achieve improved accuracy near sharp gradients or discontinuities.Moreover,to obtain a high-order of accuracy in not only space but also time,it is proposed to apply a high-order splitting scheme in time.We aim to introduce the entire SL algorithm with high-order splitting in time and high-order WENO reconstruction in space to solve the Vlasov-Poisson system.Some numerical experiments are presented to demonstrate robustness of the proposed method in having a high-order of convergence and in capturing non-smooth solutions.A key observation is that the method can capture phase structure that require twice the resolution with a polynomial based method.In 6D,this would represent a signifcant savings.
基金supported by the Spanish MICINN project MTM2013-43745-R and MTM2017-86459-Rthe Xunta de Galicia+1 种基金the FEDER under research project ED431C 2017/60-014supported by PRODEP project UAM-PTC-669
文摘Sediment transport can be modelled using hydrodynamic models based on shallow water equations coupled with the sediment concentration conservation equation and the bed con-servation equation.The complete system of equations is made up of the energy balance law and the Exner equations.The numerical solution for this complete system is done in a seg-regated manner.First,the hyperbolic part of the system of balance laws is solved using a finite volume scheme.Three ways to compute the numerical flux have been considered,the Q-scheme of van Leer,the HLLCS approximate Riemann solver,and the last one takes into account the presence of non-conservative products in the model.The discretisation of the source terms is carried out according to the numerical flux chosen.In the second stage,the bed conservation equation is solved by using the approximation computed for the system of balance laws.The numerical schemes have been validated making comparisons between the obtained numerical results and the experimental data for some physical experiments.The numerical results show a good agreement with the experimental data.
文摘In Mobile Communication Systems, inter-cell interference becomes one of the challenges that degrade the system’s performance, especially in the region with massive mobile users. The linear precoding schemes were proposed to mitigate interferences between the base stations (inter-cell). These schemes are categorized into linear and non-linear;this study focused on linear precoding schemes, which are grounded into three types, namely Zero Forcing (ZF), Block Diagonalization (BD), and Signal Leakage Noise Ratio (SLNR). The study included the Cooperative Multi-cell Multi Input Multi Output (MIMO) System, whereby each Base Station serves more than one mobile station and all Base Stations on the system are assisted by each other by shared the Channel State Information (CSI). Based on the Multi-Cell Multiuser MIMO system, each Base Station on the cell is intended to maximize the data transmission rate by its mobile users by increasing the Signal Interference to Noise Ratio after the interference has been mitigated due to the usefully of linear precoding schemes on the transmitter. Moreover, these schemes used different approaches to mitigate interference. This study mainly concentrates on evaluating the performance of these schemes through the channel distribution models such as Ray-leigh and Rician included in the presence of noise errors. The results show that the SLNR scheme outperforms ZF and BD schemes overall scenario. This implied that when the value of SNR increased the performance of SLNR increased by 21.4% and 45.7% for ZF and BD respectively.
基金This work was supported by National Key R&D Program of China(Grant Numbers 2020YFB1005900,2022YFB3305802).
文摘Due to the anonymity of blockchain,frequent security incidents and attacks occur through it,among which the Ponzi scheme smart contract is a classic type of fraud resulting in huge economic losses.Machine learningbased methods are believed to be promising for detecting ethereum Ponzi schemes.However,there are still some flaws in current research,e.g.,insufficient feature extraction of Ponzi scheme smart contracts,without considering class imbalance.In addition,there is room for improvement in detection precision.Aiming at the above problems,this paper proposes an ethereum Ponzi scheme detection scheme through opcode context analysis and adaptive boosting(AdaBoost)algorithm.Firstly,this paper uses the n-gram algorithm to extract more comprehensive contract opcode features and combine them with contract account features,which helps to improve the feature extraction effect.Meanwhile,adaptive synthetic sampling(ADASYN)is introduced to deal with class imbalanced data,and integrated with the Adaboost classifier.Finally,this paper uses the improved AdaBoost classifier for the identification of Ponzi scheme contracts.Experimentally,this paper tests our model in real-world smart contracts and compares it with representative methods in the aspect of F1-score and precision.Moreover,this article compares and discusses the state of art methods with our method in four aspects:data acquisition,data preprocessing,feature extraction,and classifier design.Both experiment and discussion validate the effectiveness of our model.
文摘We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.
基金sponsored by the National Natural Science Foundation of China under Grant No.52206101Shanghai Sailing Program under Grant No.20YF1431200the Experiments for Space Exploration Program and the Qian Xuesen Laboratory,China Academy of Space Technology under Grant No.TKTSPY-2020-01-01.
文摘There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity scheme(IVD scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall(MPB-C scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes(MPB-W scheme)and the geometric formulation scheme(GF scheme).But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past.In this paper,the numerical stability and accuracy of these schemes are clarified for the first time,by applying the five widely used contact angle schemes to simulate a two-dimensional(2D)sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively.(i)It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle,but the simulated contact angles by the PB scheme,IVD scheme,MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength.The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios.(ii)Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes,the magnitude of the spurious velocity in the PB scheme,IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme.(iii)The fluid density variation near the wall in the PB scheme is the most significant,and the variation can be diminished in the IVD scheme,MPB-C scheme andMPBWscheme.The variation totally disappeared in the GF scheme.(iv)For the simulation of capillary imbibition,the MPB-C scheme,MPB-Wscheme and GF scheme simulate the dynamics of the liquid-vapor interface well,with the GF scheme being the most accurate.The accuracy of the IVD scheme is low at a small contact angle(44 degrees)but gets high at a large contact angle(60 degrees).However,the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface.As a whole,it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting,while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.
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.
文摘In this paper, we are going to derive four numerical methods for solving the Modified Kortweg-de Vries (MKdV) equation using fourth Pade approximation for space direction and Crank Nicolson in the time direction. Two nonlinear schemes and two linearized schemes are presented. All resulting schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities are used to highlight the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be also conducted. The numerical results show that the interaction behavior is elastic and the conserved quantities are conserved exactly, and this is a good indication of the reliability of the schemes which we derived. A comparison with some existing is presented as well.
基金The project supported by the National Natural Science Foundation of China (19582007) Partly by State Key Laboratory of Scientific/Engineering Computing
文摘By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presentedin this paper by using suitable weights instead of the minmod functions appearingin various TVD schemes. Numerical comparisons between the weighted schemes andthe non-weighted schemes have been done for scalar equation, one-dimensional Eulerequations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokesequations.
基金National Natural Science Foundation of China(41375033,41225018)National Basic Research Program of China(973 Program)(2013CB430100)Fundamental Research Funds for Central Universities of Lanzhou University(LZUJBKY-2013-K16)
文摘The formation and development of typhoons are closely related to the disturbed low vortexes at the planetary boundary layer(PBL). The effects of five PBL parameterization schemes(PBL schemes hereinafter) on the trajectory,intensity, and distribution of physical quantities are studied using the mesoscale WRF model on Super Typhoon Sanba(2012) during its initial stage. Results show that the five PBL schemes exhibit significant different effects on the simulated intensity and path. The results simulated by QNSE and ACM2 without the Bogus method are close to the best track data in the numerical experiments. When the Bogus method is adopted, the simulated trajectories improve significantly because the initial field is close to the true data. Among the five PBL schemes, QNSE and ACM2 with the Bogus method present improved simulated path and intensity compared with the three other schemes. This finding indicates that the two schemes deal with the initial PBL process satisfactorily, especially in the formation and development of disturbed low vortexes. The differences in the treatment methods of the five PBL schemes affect the surface layer physical quantities and the middle and upper atmospheres during the middle to late periods of the typhoon.Although QNSE and ACM2 present better simulation results than other schemes, they exhibit a few differences in the internal structure of the typhoon. The results simulated by MYJ are worse, and this method may be unsuitable for studying the formation and development of typhoons.
文摘This paper evaluates the skills of physical Parameterization schemes in simulating extreme rainfall events over Dar es Salaam Region, Tanzania using the Weather Research and Forecasting (WRF) model. The model skill is determined during the 21 December 2011 flooding event. Ten sensitivity experiments have been conducted using Cumulus, Convective and Planetary boundary layer schemes to find the best combination and optimize the WRF model for the study area for heavy rainfall events. Model simulation results were verified against observed data using standard statistical tests. The model simulations show encouraging and better statistical results with the combination of Kain-Fritsch cumulus parameterization scheme, Lin microphysics scheme and Asymmetric Convection Model 2 (ACM2) planetary boundary scheme than any other combinations of physical parameterization schemes over Dar es Salaam region.
文摘In this paper, we present a study of thermal, average power scaling, change in index of refraction and stress in photonic crystal fiber lasers with different pump schemes: forward pump scheme, backward pump scheme, forward pump scheme with reflection of 98%, backward pump scheme with reflection of 98% and bi-directional pump scheme. We show that management of thermal effects in fiber lasers will determine the efficiency and success of scaling-up efforts. In addition, we show that the most suitable scheme is the bi-directional.
基金supported jointly by the Projects of Jiangsu Key Lab of Meteorological Disaster (Grant No. Klme060207)the National Natural Science Foundation of China (Grant No. 40875031)
文摘The mei-yu front heavy rainstorms occurred over Nanjing on 3 5 and 8 9 July 2003 and were simulated in this paper using the Weather Research and Forecasting Model (WRFv3.1) with various mesoscale convection parameterization schemes (MCPSs). The simulations show that the temporal and spatial evolution and distribution of rainstorms can be modeled; however, there was incongruity between the comparative simulations of four different MCPSs and the observed data. These disparities were exhibited in the simulations of both the 24-hour surface rainfall total and the hourly precipitation rate. Further analysis revealed that the discrepancies of vertical velocity and the convective vorticity vector (CVV) between the four simulations were attributed to the deviation of rainfall values. In addition, the simulations show that the mid-scale convection, particularly the mesoscale convection system (MCS) formation, can be well simulated with the proper mesoscale convection parameterization schemes and may be a crucial factor of the mei-yu front heavy rainstorm. These results suggest that, in an effort to enhance simulation and prediction of heavy rainfall and rainstorms, subsequent studies should focus on the development and improvement of MCPS.
文摘In order to investigate parameters of FAE (fuel air explosive) explosion, the two_phase gas_droplet conservation equations with two_dimensional axial symmetry in the Euler coordinate were used. High_resolution implicit TVD (total variation diminishing) schemes were applied to gas phase equations and MacCormack schemes to liquid equations. The for mation and propagation of gas_droplet detonation wave were simulated numerically. The simulation results and the others are compared with a good agreement.
文摘Various control schemes of automobile pollution are comprehensively evaluated by using the weighting and feyzzy methods, from which several feasible schemes are selected, and then mulit-target decision is made by using the minimum distance and hierarcby analysis methods, for determining the optimal control methods of automobile pollution.
文摘Two kinds of symplectic schemes are proposed for the equations of vortex system in half plane.One is the Reflecting-method which is based on the symplectic schemes for the system in the whole plane.The other is constructed directly according to the feature of the system.Aseries of numerical results are presented to show the effectiveness of our schemes.
