Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ...Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.展开更多
This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary ...This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.展开更多
In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the g...In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.展开更多
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
By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod func...By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.展开更多
A new method was proposed for constructing total variation diminishing (TVD) upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can e...A new method was proposed for constructing total variation diminishing (TVD) upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD (CTVD) schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.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
The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipativ...The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were reported.The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations.The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do.Research progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.展开更多
The vertical structures of atmospheric temperature anomalies associated with El Nio are simulated with a spectrum atmospheric general circulation model developed by LASG/IAP (SAMIL). Sensitivity of the model’s resp...The vertical structures of atmospheric temperature anomalies associated with El Nio are simulated with a spectrum atmospheric general circulation model developed by LASG/IAP (SAMIL). Sensitivity of the model’s response to convection scheme is discussed. Two convection schemes, i.e., the revised Zhang and Macfarlane (RZM) and Tiedtke (TDK) convection schemes, are employed in two sets of AMIP-type (Atmospheric Model Intercomparison Project) SAMIL simulations, respectively. Despite some deficiencies in the upper troposphere, the canonical El Nio-related temperature anomalies characterized by a prevailing warming throughout the tropical troposphere are well reproduced in both simulations. The performance of the model in reproducing temperature anomalies in "atypical" El Nio events is sensitive to the convection scheme. When employing the RZM scheme, the warming center over the central-eastern tropical Pacific and the strong cooling in the western tropical Pacific at sea surface level are underestimated. The quadru-pole temperature anomalies in the middle and upper troposphere are also obscured. The result of employing the TDK scheme resembles the reanalysis and hence shows a better performance. The simulated largescale circulations associated with atypical El Nio events are also sensitive to the convection schemes. When employing the RZM scheme, SAMIL failed in capturing the classical Southern Oscillation pattern. In accordance with the unrealistic anomalous Walker circulation and the upper tropospheric zonal wind changes, the deficiencies of the precipitation simulation are also evident. These results demonstrate the importance of convection schemes in simulating the vertical structure of atmospheric temperature anomalies associated with El Nio and should serve as a useful reference for future improvement of SAMIL.展开更多
A deep foundation pit constructed for an underground transportation hub was excavated near the Yangtze River. Among the strata, there are two confined aquifers, between which lies an aquiclude that is partially missin...A deep foundation pit constructed for an underground transportation hub was excavated near the Yangtze River. Among the strata, there are two confined aquifers, between which lies an aquiclude that is partially missing. To guarantee the safety of pit excavation, the piezometric head of the upper confined aquifer, where the pit bottom is located, should be 1 m below the pit bottom, while that of the lower confined aquifer should be dewatered down to a safe water level to avoid uplift problem. The Yangtze River levee is notably close to the pit, and its deformation caused by dewatering should be controlled. A pumping test was performed to obtain the hydraulic conductivity of the upper confined aquifer. The average value of the hydraulic conductivity obtained from analytical calculation is 20.45 m/d, which is larger than the values from numerical simulation(horizontal hydraulic conductivity K_H = 16 m/d and vertical hydraulic conductivity K_V = S m/d). The difference between K_H and K_V indicates the anisotropy of the aquifer. Two dewatering schemes were designed for the construction and simulated by the numerical models for comparison purposes. The results show that though the first scheme could meet the dewatering requirements, the largest accumulated settlement and differential settlement would be94.64 mm and 3.3‰, respectively, greatly exceeding the limited values. Meanwhile, the second scheme,in which the bottoms of the waterproof curtains in ramp B and the river side of ramp A are installed at a deeper elevation of-28 m above sea level, and 27 recharge wells are set along the levee, can control the deformation of the levee significantly.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
文摘Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.
基金supported by the NSFC grant 11801143J.Lu’s research is partially supported by the NSFC grant 11901213+3 种基金the National Key Research and Development Program of China grant 2021YFA1002900supported by the NSFC grant 11801140,12171177the Young Elite Scientists Sponsorship Program by Henan Association for Science and Technology of China grant 2022HYTP0009the Program for Young Key Teacher of Henan Province of China grant 2021GGJS067.
文摘This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.
基金supported by the Simons Foundation:Collaboration Grantssupported by the AFOSR grant FA9550-18-1-0383.
文摘In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.
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 presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.
基金Project supported by the National Natural Science Foundation of China (Nos. 10172015 and 90205010)
文摘A new method was proposed for constructing total variation diminishing (TVD) upwind schemes in conservation forms. Two limiters were used to prevent nonphysical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD (CTVD) schemes were tested, one is thirdorder accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a twodimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.
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(90205027)
文摘The role of dispersions in the numerical solutions of hydrodynamic equation systems has been realized for long time.It is only during the last two decades that extensive studies on the dispersion-controlled dissipative(DCD)schemes were reported.The studies have demonstrated that this kind of the schemes is distinct from conventional dissipation-based schemes in which the dispersion term of the modified equation is not considered in scheme construction to avoid nonphysical oscillation occurring in shock wave simulations.The principle of the dispersion controlled aims at removing nonphysical oscillations by making use of dispersion characteristics instead of adding artificial viscosity to dissipate the oscillation as the conventional schemes do.Research progresses on the dispersion- controlled principles are reviewed in this paper,including the exploration of the role of dispersions in numerical simulations,the development of the dispersion-controlled principles,efforts devoted to high-order dispersion-controlled dissipative schemes,the extension to both the finite volume and the finite element methods,scheme verification and solution validation,and comments on several aspects of the schemes from author's viewpoint.
基金supported by the National Natural Science Foundation of China (40890054, 40821092, 90711004)R&D Spe-cial Fund for Public Welfare Industry (meteorol-ogy)(GYHY200706010)National Key Technologies R&D Program (2007BAC29B03)
文摘The vertical structures of atmospheric temperature anomalies associated with El Nio are simulated with a spectrum atmospheric general circulation model developed by LASG/IAP (SAMIL). Sensitivity of the model’s response to convection scheme is discussed. Two convection schemes, i.e., the revised Zhang and Macfarlane (RZM) and Tiedtke (TDK) convection schemes, are employed in two sets of AMIP-type (Atmospheric Model Intercomparison Project) SAMIL simulations, respectively. Despite some deficiencies in the upper troposphere, the canonical El Nio-related temperature anomalies characterized by a prevailing warming throughout the tropical troposphere are well reproduced in both simulations. The performance of the model in reproducing temperature anomalies in "atypical" El Nio events is sensitive to the convection scheme. When employing the RZM scheme, the warming center over the central-eastern tropical Pacific and the strong cooling in the western tropical Pacific at sea surface level are underestimated. The quadru-pole temperature anomalies in the middle and upper troposphere are also obscured. The result of employing the TDK scheme resembles the reanalysis and hence shows a better performance. The simulated largescale circulations associated with atypical El Nio events are also sensitive to the convection schemes. When employing the RZM scheme, SAMIL failed in capturing the classical Southern Oscillation pattern. In accordance with the unrealistic anomalous Walker circulation and the upper tropospheric zonal wind changes, the deficiencies of the precipitation simulation are also evident. These results demonstrate the importance of convection schemes in simulating the vertical structure of atmospheric temperature anomalies associated with El Nio and should serve as a useful reference for future improvement of SAMIL.
基金financially supported by the doctoral fund of the Ministry of Education of Chinathe Nature Science Foundation of Jiangsu Province, China (Grant Nos. 20130091110020 and BE2015675)
文摘A deep foundation pit constructed for an underground transportation hub was excavated near the Yangtze River. Among the strata, there are two confined aquifers, between which lies an aquiclude that is partially missing. To guarantee the safety of pit excavation, the piezometric head of the upper confined aquifer, where the pit bottom is located, should be 1 m below the pit bottom, while that of the lower confined aquifer should be dewatered down to a safe water level to avoid uplift problem. The Yangtze River levee is notably close to the pit, and its deformation caused by dewatering should be controlled. A pumping test was performed to obtain the hydraulic conductivity of the upper confined aquifer. The average value of the hydraulic conductivity obtained from analytical calculation is 20.45 m/d, which is larger than the values from numerical simulation(horizontal hydraulic conductivity K_H = 16 m/d and vertical hydraulic conductivity K_V = S m/d). The difference between K_H and K_V indicates the anisotropy of the aquifer. Two dewatering schemes were designed for the construction and simulated by the numerical models for comparison purposes. The results show that though the first scheme could meet the dewatering requirements, the largest accumulated settlement and differential settlement would be94.64 mm and 3.3‰, respectively, greatly exceeding the limited values. Meanwhile, the second scheme,in which the bottoms of the waterproof curtains in ramp B and the river side of ramp A are installed at a deeper elevation of-28 m above sea level, and 27 recharge wells are set along the levee, can control the deformation of the levee significantly.
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.