Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple the...Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.展开更多
In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton ...In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.展开更多
A method for static aeroelastic analysis based on the high-order panel method and modal method is presented. The static aeroelastic characteristics of flexible wings are investigated using this method. Three-dimension...A method for static aeroelastic analysis based on the high-order panel method and modal method is presented. The static aeroelastic characteristics of flexible wings are investigated using this method. Three-dimensional aerodynamic models of flexible wings are constructed based on the geometry of wing configuration, and the modal method is adopted to achieve the fluid-structure coupling. The static aeroelastic characteristics of the AGARD445.6 wing and a low-aspect-ratio wing are investigated in this study. The influences of elastic structural deformation on aerodynamic forces are studied with an emphasis analyzing the aerodynamic coefficients, wing root loads, structural deformation and pressure distribution of different sections, and results are compared with the results from wind-tunnel tests and the elastic results based on experimental aerodynamic forces. It is concluded that aerodynamic forces can be accurately calculated with the high-order panel method. The method presented in this study is feasible, credible and efficient. Comprehensive static aeroelastic characteristics can be provided by the method for early phases of aircraft design.展开更多
To reduce the risk of mission failure caused by the MM/OD impact of the spacecraft,it is necessary to optimize the design of the spacecraft.Spacecraft survivability assessment is the key technology in the optimal desi...To reduce the risk of mission failure caused by the MM/OD impact of the spacecraft,it is necessary to optimize the design of the spacecraft.Spacecraft survivability assessment is the key technology in the optimal design of spacecraft.Spacecraft survivability assessment includes spacecraft impact sensitivity analysis and spacecraft component vulnerability analysis under MM/OD environment.The impact sensitivity refers to the probability of a spacecraft encountering an MM/OD impact while in orbit.Vulnerability refers to the probability that each component of a spacecraft may fail or malfunction when impacted by space debris.Yet this paper mainly analyzes the impact sensitivity and proposes a spacecraft sensitivity assessment method under the MM/OD environment based on a panel method.Under this panel method,a spacecraft geometric model is discretized into small panels,and whether they are impacted by MM/OD or not is determined through the analysis of the shielding or shadowing relationships between panels.The number of impacts on each panel is obtained through calculation,and accordingly the probability of each spacecraft component encountering MM/OD impact can be acquired,thus generating the impact sensibility.This paper extracts data from the NASA’s ORDEM2000,the ESA’s MASTER8 as well as the SDEEM2015(Space Debris Environmental Engineering Model developed by HIT),and uses the PCHIP(Piecewise Cubic Hermite Interpolating Polynomial)method to interpolate and fit the size-flux relationship of space debris.Compared with linear interpolation and cubic spline interpolation,the fitting results through the method are relatively more accurate.The feasibility of this method is also demonstrated through two actual examples shown in this paper,whose results are close to those from ESABASE,although there are some minor errors mainly due to different debris data input.Through the cross-check by three risk assessment software-BUMPER,MDPANTO and MODAOST-under standard operating conditions,the feasibility of this method is again verified.展开更多
The Runge-Kutta discontinuous Galerkin finite element method (RK-DGFEM) is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and ...The Runge-Kutta discontinuous Galerkin finite element method (RK-DGFEM) is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method (FVM). RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic (TM) wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.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
To make three-dimensional electromagnetic exploration achievable,the distributed wide field electromagnetic method(WFEM)based on the high-order 2^(n) sequence pseudo-random signal is proposed and realized.In this meth...To make three-dimensional electromagnetic exploration achievable,the distributed wide field electromagnetic method(WFEM)based on the high-order 2^(n) sequence pseudo-random signal is proposed and realized.In this method,only one set of high-order pseudo-random waveforms,which contains all target frequencies,is needed.Based on high-order sequence pseudo-random signal construction algorithm,the waveform can be customized according to different exploration tasks.And the receivers are independent with each other and dynamically adjust the acquisition parameters according to different requirements.A field test in the deep iron ore of Qihe−Yucheng showed that the distributed WFEM based on high-order pseudo-random signal realizes the high-efficiency acquisition of massive electromagnetic data in quite a short time.Compared with traditional controlled-source electromagnetic methods,the distributed WFEM is much more efficient.Distributed WFEM can be applied to the large scale and high-resolution exploration for deep resources and minerals.展开更多
A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a G...A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger (NLS) equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.展开更多
This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been...This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.展开更多
This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton)...This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton) solutions and multiple-singular-kink (soliton) solutions are derived for the two equations.展开更多
Nystrm method is a new method for solving electromagnetic scattering problems. This paper gives the detailed description on high-order Nystrm method used for the electric field integral equation of electromagnetic sca...Nystrm method is a new method for solving electromagnetic scattering problems. This paper gives the detailed description on high-order Nystrm method used for the electric field integral equation of electromagnetic scattering problems. The numerical solutions of two examples are correct compared with Method Of Moment(MOM).展开更多
This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept...This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.展开更多
The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew(ZSC), J. Comput. Phys. 218, 353(2006)]is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass cons...The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew(ZSC), J. Comput. Phys. 218, 353(2006)]is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out,including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.展开更多
An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. I...An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher ? order simulations(fourth ? and fifth ? order accuracy) are adopted.Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher?order DG method's better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom(DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.展开更多
A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order pro...A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.展开更多
An effective numerical model for wave propagation over three-dimensional(3D)bathymetry was developed based on the High-Order Spectral(HOS)method and combined with a moving bottom boundary.Based on this model,tsunami w...An effective numerical model for wave propagation over three-dimensional(3D)bathymetry was developed based on the High-Order Spectral(HOS)method and combined with a moving bottom boundary.Based on this model,tsunami waves caused by various mechanisms were simulated and analyzed.Two-dimensional bed upthrust and the effect of the uplift velocity of the bathymetry on the wave profiles of tsunami waves were studied.Next,tsunami waves caused by 3D submarine slides were generated and the effects of the slide velocity,slide dimension and water depth on the tsunami waves were analyzed.Based on wavelet analysis,the properties of the tsunami wave propagation were investigated.The results show that the bottom movement can significantly affect the generation and propagation of tsunami waves and the studies could help understand the mechanisms of tsunamis caused by a moving bottom boundary.展开更多
A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell's equations is introduced and analyzed. The pro- posed method combines a centered approximation for the eval...A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell's equations is introduced and analyzed. The pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwelrs equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high- order elements show the potential of the method.展开更多
The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi...The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.展开更多
In this paper, a family of high-order compact finite difference methods in combination preconditioned methods are used for solution of the Diffusion-Convection equation. We developed numerical methods by replacing the...In this paper, a family of high-order compact finite difference methods in combination preconditioned methods are used for solution of the Diffusion-Convection equation. We developed numerical methods by replacing the time and space derivatives by compact finite-difference approximations. The system of resulting nonlinear finite difference equations are solved by preconditioned Krylov subspace methods. Numerical results are given to verify the behavior of high-order compact approximations in combination preconditioned methods for stability, convergence. Also, the accuracy and efficiency of the proposed scheme are considered.展开更多
An efficient high-order immersed interface method (IIM) is proposed to solve two-dimensional (2D) heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in ...An efficient high-order immersed interface method (IIM) is proposed to solve two-dimensional (2D) heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact (HOC) difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit (ADI) scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.展开更多
基金supported by the NSFC Grant no.12271492the Natural Science Foundation of Henan Province of China Grant no.222300420550+1 种基金supported by the NSFC Grant no.12271498the National Key R&D Program of China Grant no.2022YFA1005202/2022YFA1005200.
文摘Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.
文摘In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60736025, 90716006 and 10902006)the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 20091102110015)the Major Programs of China National Space Administration (Grant No. D2120060013)
文摘A method for static aeroelastic analysis based on the high-order panel method and modal method is presented. The static aeroelastic characteristics of flexible wings are investigated using this method. Three-dimensional aerodynamic models of flexible wings are constructed based on the geometry of wing configuration, and the modal method is adopted to achieve the fluid-structure coupling. The static aeroelastic characteristics of the AGARD445.6 wing and a low-aspect-ratio wing are investigated in this study. The influences of elastic structural deformation on aerodynamic forces are studied with an emphasis analyzing the aerodynamic coefficients, wing root loads, structural deformation and pressure distribution of different sections, and results are compared with the results from wind-tunnel tests and the elastic results based on experimental aerodynamic forces. It is concluded that aerodynamic forces can be accurately calculated with the high-order panel method. The method presented in this study is feasible, credible and efficient. Comprehensive static aeroelastic characteristics can be provided by the method for early phases of aircraft design.
基金supported by the National Natural Science Foundation of China(Grant No.11772113)。
文摘To reduce the risk of mission failure caused by the MM/OD impact of the spacecraft,it is necessary to optimize the design of the spacecraft.Spacecraft survivability assessment is the key technology in the optimal design of spacecraft.Spacecraft survivability assessment includes spacecraft impact sensitivity analysis and spacecraft component vulnerability analysis under MM/OD environment.The impact sensitivity refers to the probability of a spacecraft encountering an MM/OD impact while in orbit.Vulnerability refers to the probability that each component of a spacecraft may fail or malfunction when impacted by space debris.Yet this paper mainly analyzes the impact sensitivity and proposes a spacecraft sensitivity assessment method under the MM/OD environment based on a panel method.Under this panel method,a spacecraft geometric model is discretized into small panels,and whether they are impacted by MM/OD or not is determined through the analysis of the shielding or shadowing relationships between panels.The number of impacts on each panel is obtained through calculation,and accordingly the probability of each spacecraft component encountering MM/OD impact can be acquired,thus generating the impact sensibility.This paper extracts data from the NASA’s ORDEM2000,the ESA’s MASTER8 as well as the SDEEM2015(Space Debris Environmental Engineering Model developed by HIT),and uses the PCHIP(Piecewise Cubic Hermite Interpolating Polynomial)method to interpolate and fit the size-flux relationship of space debris.Compared with linear interpolation and cubic spline interpolation,the fitting results through the method are relatively more accurate.The feasibility of this method is also demonstrated through two actual examples shown in this paper,whose results are close to those from ESABASE,although there are some minor errors mainly due to different debris data input.Through the cross-check by three risk assessment software-BUMPER,MDPANTO and MODAOST-under standard operating conditions,the feasibility of this method is again verified.
文摘The Runge-Kutta discontinuous Galerkin finite element method (RK-DGFEM) is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method (FVM). RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic (TM) wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.
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funded by the National Natural Science Foundation of China(No.42004056)the Natural Science Foundation of Shangdong Province,China(No.ZR2020QD052)China Postdoctoral Science Foundation(No.2019M652386)。
文摘To make three-dimensional electromagnetic exploration achievable,the distributed wide field electromagnetic method(WFEM)based on the high-order 2^(n) sequence pseudo-random signal is proposed and realized.In this method,only one set of high-order pseudo-random waveforms,which contains all target frequencies,is needed.Based on high-order sequence pseudo-random signal construction algorithm,the waveform can be customized according to different exploration tasks.And the receivers are independent with each other and dynamically adjust the acquisition parameters according to different requirements.A field test in the deep iron ore of Qihe−Yucheng showed that the distributed WFEM based on high-order pseudo-random signal realizes the high-efficiency acquisition of massive electromagnetic data in quite a short time.Compared with traditional controlled-source electromagnetic methods,the distributed WFEM is much more efficient.Distributed WFEM can be applied to the large scale and high-resolution exploration for deep resources and minerals.
基金supported by the National Natural Science Foundation of China(Nos.11502103 and11421062)the Open Fund of State Key Laboratory of Structural Analysis for Industrial Equipment of China(No.GZ15115)
文摘A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger (NLS) equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.
基金supported by an Early Career Faculty grant from NASA's Space Technology Research Grants Programprovided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center
文摘This article focuses on the development of a discontinuous Galerkin (DG) method for simulations of multicomponent and chemically reacting flows. Compared to aerodynamic flow applications, in which DG methods have been successfully employed, DG simulations of chemically reacting flows introduce challenges that arise from flow unsteadiness, combustion, heat release, compressibility effects, shocks, and variations in thermodynamic properties. To address these challenges, algorithms are developed, including an entropy-bounded DG method, an entropy-residual shock indicator, and a new formulation of artificial viscosity. The performance and capabilities of the resulting DG method are demonstrated in several relevant applications, including shock/bubble interaction, turbulent combustion, and detonation. It is concluded that the developed DG method shows promising performance in application to multicomponent reacting flows. The paper concludes with a discussion of further research needs to enable the application of DG methods to more complex reacting flows.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10871117 and 10571110)
文摘This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton) solutions and multiple-singular-kink (soliton) solutions are derived for the two equations.
基金Supported by the National Natural Science Fbundation of China(No.60371003)
文摘Nystrm method is a new method for solving electromagnetic scattering problems. This paper gives the detailed description on high-order Nystrm method used for the electric field integral equation of electromagnetic scattering problems. The numerical solutions of two examples are correct compared with Method Of Moment(MOM).
基金Sponsored by the National Natural Science Foundation of China(Grant No.50508012)
文摘This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11862003 and 81860635)the Key Project of the Natural Science Foundation of Guangxi Zhuang Autonomous Region,China(Grant No.2017GXNSFDA198038)+3 种基金the Project of Natural Science Foundation of Guangxi Zhuang Autonomous Region,China(Grant No.2018GXNSFAA281302)the Project for Promotion of Young and Middle-aged Teachers’Basic Scientific Research Ability in Guangxi Universities,China(Grant No.2019KY0084)the“Bagui Scholar”Teams for Innovation and Research Project of Guangxi Zhuang Autonomous Region,Chinathe Graduate Innovation Program of Guangxi Normal University,China(Grant No.JXYJSKT-2019-007)。
文摘The Z–S–C multiphase lattice Boltzmann model [Zheng, Shu, and Chew(ZSC), J. Comput. Phys. 218, 353(2006)]is favored due to its good stability, high efficiency, and large density ratio. However, in terms of mass conservation, this model is not satisfactory during the simulation computations. In this paper, a mass correction is introduced into the ZSC model to make up the mass leakage, while a high-order difference is used to calculate the gradient of the order parameter to improve the accuracy. To verify the improved model, several three-dimensional multiphase flow simulations are carried out,including a bubble in a stationary flow, the merging of two bubbles, and the bubble rising under buoyancy. The numerical simulations show that the results from the present model are in good agreement with those from previous experiments and simulations. The present model not only retains the good properties of the original ZSC model, but also achieves the mass conservation and higher accuracy.
基金co-supported by the National High Technology Research and Development Program of China(No.2015AA015303)the National Natural Science Foundation of China(No.11272152)+1 种基金the Aeronautical Science Foundation of China(No.20152752033)the Open Project of Key Laboratory of Aerodynamic Noise Control
文摘An implicit higher ? order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher ? order simulations(fourth ? and fifth ? order accuracy) are adopted.Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher?order DG method's better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom(DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.
文摘A uniform high-order method is. presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems ( 1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O (hm+1) accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O (hm+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.
基金This study was financially supported by the National Natural Science Foundation of China(Grant Nos.51739010 and 51879037).
文摘An effective numerical model for wave propagation over three-dimensional(3D)bathymetry was developed based on the High-Order Spectral(HOS)method and combined with a moving bottom boundary.Based on this model,tsunami waves caused by various mechanisms were simulated and analyzed.Two-dimensional bed upthrust and the effect of the uplift velocity of the bathymetry on the wave profiles of tsunami waves were studied.Next,tsunami waves caused by 3D submarine slides were generated and the effects of the slide velocity,slide dimension and water depth on the tsunami waves were analyzed.Based on wavelet analysis,the properties of the tsunami wave propagation were investigated.The results show that the bottom movement can significantly affect the generation and propagation of tsunami waves and the studies could help understand the mechanisms of tsunamis caused by a moving bottom boundary.
基金supported by a grant from the French National Ministry of Education and Research(MENSR,19755-2005)
文摘A high-order leap-frog based non-dissipative discontinuous Galerkin time- domain method for solving Maxwell's equations is introduced and analyzed. The pro- posed method combines a centered approximation for the evaluation of fluxes at the in- terface between neighboring elements, with a Nth-order leap-frog time scheme. More- over, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwelrs equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with high- order elements show the potential of the method.
文摘The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.
文摘In this paper, a family of high-order compact finite difference methods in combination preconditioned methods are used for solution of the Diffusion-Convection equation. We developed numerical methods by replacing the time and space derivatives by compact finite-difference approximations. The system of resulting nonlinear finite difference equations are solved by preconditioned Krylov subspace methods. Numerical results are given to verify the behavior of high-order compact approximations in combination preconditioned methods for stability, convergence. Also, the accuracy and efficiency of the proposed scheme are considered.
基金supported by the National Natural Science Foundation of China(No.51174236)the National Basic Research Program of China(973 Program)(No.2011CB606306)the Opening Project of State Key Laboratory of Porous Metal Materials(No.PMM-SKL-4-2012)
文摘An efficient high-order immersed interface method (IIM) is proposed to solve two-dimensional (2D) heat problems with fixed interfaces on Cartesian grids, which has the fourth-order accuracy in the maximum norm in both time and space directions. The space variable is discretized by a high-order compact (HOC) difference scheme with correction terms added at the irregular points. The time derivative is integrated by a Crank-Nicolson and alternative direction implicit (ADI) scheme. In this case, the time accuracy is just second-order. The Richardson extrapolation method is used to improve the time accuracy to fourth-order. The numerical results confirm the convergence order and the efficiency of the method.