We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-or...We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.展开更多
Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the...Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.展开更多
A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncatio...A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncation error is O（△t^2 ＋ △x^4）.展开更多
In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stabili...In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.展开更多
The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order sy...The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.展开更多
In order to study complicated interacting flow field over projectile with lateral jets. External interacting turbulence flow over projectile with lateral jets was numerically simulated firstly in supersonic speed and ...In order to study complicated interacting flow field over projectile with lateral jets. External interacting turbulence flow over projectile with lateral jets was numerically simulated firstly in supersonic speed and zero attack angle. The three dimensional Reynolds averaged Navier Stokes equations and implicit finite volume TVD scheme were applied. In order to avoid zonal method, ’O’ type grid of single zone including projectile base was produced by algebraic arithmetic. Body fitted grid was generated for the lateral nozzle exit successfully so that the nozzle exit can be simulated more accurately. The high Reynolds number two equation κ ε turbulence models were used. The main features of the complex flow are captured. The two kinds of flow field over projectile with and without lateral jets are compared from shock structure, pressure of body and base, etc . It shows that lateral jets not only can provide push force, but also change aerodynamics characteristic of projectile significantly. The results are very important for the study of projectile with lateral rocket boosters.展开更多
We study the hyperbolic–parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, ...We study the hyperbolic–parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed.展开更多
The time-dependent Schrodinger equation(TDSE) is usually treated in the real space in the textbook.However,it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast osc...The time-dependent Schrodinger equation(TDSE) is usually treated in the real space in the textbook.However,it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast oscillation of the electron wave packets under the interaction of intense laser fields.Here we demonstrate that the TDSE can be efficiently solved in the momentum space.The high-order harmonic generation and above-threshold ionization spectra obtained by numerical solutions of TDSE in momentum space agree well with previous studies in real space,but significantly reducing the computation cost.展开更多
Two interface capturing methods are studied for multi fluid flows, governed by the stiffened gas equation of state. The mixture type interface capturing algorithm uses a simple volume fraction model Euler equations wr...Two interface capturing methods are studied for multi fluid flows, governed by the stiffened gas equation of state. The mixture type interface capturing algorithm uses a simple volume fraction model Euler equations written in a quasi conservative form, which is solved by a standard high resolution piecewise parabolic method (PPM) with multi fluid Riemann solver. The level set interface capturing method uses a narrow band ghost fluid method (GFM) with no numerical smearing. Several examples are presented and compared for one and two dimensions, which show the feasibility of the two methods applied to various multi fluid problems.展开更多
In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and t...In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.展开更多
By conjugating features of combustion gas jetting flows of the solid-rocket and using mathematical methods, a numerical scheme is systematically derived based on Harten′s standard TVD scheme, which fits for the flow ...By conjugating features of combustion gas jetting flows of the solid-rocket and using mathematical methods, a numerical scheme is systematically derived based on Harten′s standard TVD scheme, which fits for the flow with high temperature, pressure and velocity. The rational calculation formula of pressure partial derivation is also given out. By using the chemical kinetics knowledge, problems of multi-component and finite rate chemical reaction contained in combustion gas of the rocket flow field are discussed. The method for solving the mass source term of chemical reaction is clarified. Taking 9 reaction equations with 12 components as an example and utilizing the established calculation program, the free jetting flow field of the rocket is simulated. Numerical results show the correctness of the numerical scheme.展开更多
为研究颗粒阻尼器布置方案对多层结构减震性能的影响,制作了缩尺比为1/5的三层钢框架模型结构,进行了5条天然波下的地震模拟振动台试验,研究并联式单向单颗粒阻尼器(Parallel Single-dimensional Single Particle Damper,PSSPD)的减震...为研究颗粒阻尼器布置方案对多层结构减震性能的影响,制作了缩尺比为1/5的三层钢框架模型结构,进行了5条天然波下的地震模拟振动台试验,研究并联式单向单颗粒阻尼器(Parallel Single-dimensional Single Particle Damper,PSSPD)的减震控制效果。基于试验获得的模型自振频率、阻尼比等动力特性设计3种PSSPD布置方案,分析不同布置方案下模型结构的试验现象及位移和加速度响应。试验结果表明:PSSPD对结构响应峰值减震率可达到43.43%,均方根减震率可达到38.18%,其对多层结构具有良好的减震控制效果;PSSPD对结构均方根的平均减震效果要优于对峰值的平均减震效果;PSSPD布置方案对其减震效果影响显著,且其减震性能与本身参数、受控结构振动特性、地震动参数之间的耦合关系复杂。最后,建立PSSPD在任意布置方案下受控结构的力学模型,提出其数值分析流程。数值计算结果和试验结果在位移峰值及均方根方面具有良好的吻合度。展开更多
Semisubmersible naval ships are versatile military crafts that combine the advantageous features of high-speed planing crafts and submarines.At-surface,these ships are designed to provide sufficient speed and maneuver...Semisubmersible naval ships are versatile military crafts that combine the advantageous features of high-speed planing crafts and submarines.At-surface,these ships are designed to provide sufficient speed and maneuverability.Additionally,they can perform shallow dives,offering low visual and acoustic detectability.Therefore,the hydrodynamic design of a semisubmersible naval ship should address at-surface and submerged conditions.In this study,Numerical analyses were performed using a semisubmersible hull form to analyze its hydrodynamic features,including resistance,powering,and maneuvering.The simulations were conducted with Star CCM+version 2302,a commercial package program that solves URANS equations using the SST k-ωturbulence model.The flow analysis was divided into two parts:at-surface simulations and shallowly submerged simulations.At-surface simulations cover the resistance,powering,trim,and sinkage at transition and planing regimes,with corresponding Froude numbers ranging from 0.42 to 1.69.Shallowly submerged simulations were performed at seven different submergence depths,ranging from D/LOA=0.0635 to D/LOA=0.635,and at two different speeds with Froude numbers of 0.21 and 0.33.The behaviors of the hydrodynamic forces and pitching moment for different operation depths were comprehensively analyzed.The results of the numerical analyses provide valuable insights into the hydrodynamic performance of semisubmersible naval ships,highlighting the critical factors influencing their resistance,powering,and maneuvering capabilities in both at-surface and submerged conditions.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570the Open Foundation of State Key Laboratory of High Performance Computing of China+1 种基金the Research Fund of National University of Defense Technology under Grant No JC15-02-02the Fund from HPCL
文摘We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.
基金Supported by the National Natural Defense Basic Scientific Research Program of China(A262006-1288)the Key Disciplines Program of Shanghai Municipal Commission of Education(J50501)~~
文摘Supersonic axisymmetric jet flow over a missile afterbody containing exhaust jet is simulated using the second order accurate positive schemes method developed for solving the axisymmetric Euler equations based on the 2-D conservation laws.Comparisons between the numerical results and the experimental measurements show excellent agreements.The computed results are in good agreement with the numerical solutions obtained by using third order accurate RKDG finite element method.The results show larger gradient at discontinuous points compared with those obtained by second order accurate TVD schemes.It indicates that the presented method is efficient and reliable for solving the axisymmetric jet with external freestream flows,and shows that the method captures shocks well without numerical noise.
基金NSF of the Education Department of Henan Province(20031100010)
文摘A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncation error is O（△t^2 ＋ △x^4）.
基金the National Natural Science Foundation of China(No.49925412,49990450),the National Basic Research Science Foundation(No.G2000078405)
文摘In this paper, a new numerical scheme of Total Variation Diminishing (TVD) MacCormack type for MagnetoHydroDynamic (MHD) equations is proposed by taking into account of the characteristics such as convergence, stability, resolution. This new scheme is established by solving the MHD equations with a TVD modified MacCormack scheme for the purpose of developing a scheme of quick convergence as well as of TVD property. To show the validation, simplicity and practicability of the scheme for modelling MHD problems, a self-similar Cauchy problem with the discontinuous initial data consisting of constant states, and the collision of two fast MHD shocks, and two-dimensional Orszag and Tang's MHD vortex problem are discussed with the numerical results conforming to the existing results obtained by the Roe type TVD, the high-order Godunov scheme,and Weighted Essentially Non-Oscillatory (WENO) scheme. The numerical tests show that this two-step TVD MacCormack numerical scheme for MHD system is of robust operation in the presence of very strong waves, thin shock fronts, thin contact and slip surface discontinuities.
基金supported by the National Natural Science Foundation of China(Grant Nos.60931002 and 61101064)the Universities Natural Science Foundation of Anhui Province,China(Grant Nos.KJ2011A002 and 1108085J01)
文摘The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.
文摘In order to study complicated interacting flow field over projectile with lateral jets. External interacting turbulence flow over projectile with lateral jets was numerically simulated firstly in supersonic speed and zero attack angle. The three dimensional Reynolds averaged Navier Stokes equations and implicit finite volume TVD scheme were applied. In order to avoid zonal method, ’O’ type grid of single zone including projectile base was produced by algebraic arithmetic. Body fitted grid was generated for the lateral nozzle exit successfully so that the nozzle exit can be simulated more accurately. The high Reynolds number two equation κ ε turbulence models were used. The main features of the complex flow are captured. The two kinds of flow field over projectile with and without lateral jets are compared from shock structure, pressure of body and base, etc . It shows that lateral jets not only can provide push force, but also change aerodynamics characteristic of projectile significantly. The results are very important for the study of projectile with lateral rocket boosters.
基金Project supported by the National Natural Science Foundation of China(Grant No.11471262)the National Basic Research Program of China(Grant No.2012CB025904)the State Key Laboratory of Science and Engineering Computing and the Center for High Performance Computing of Northwestern Polytechnical University,China
文摘We study the hyperbolic–parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed.
基金Project supported by the National Key Research and Development Program of China(Grant No.2019YFA0307702)the National Natural Science Foundation of China(Grants Nos.91850121 and 11674363)+1 种基金the Science Fund of Educational Department of Henan Province of China(Grant No.2011C140001)the Ninth Group of Key Disciplines in Henan Province,China(Grant No.2018119).
文摘The time-dependent Schrodinger equation(TDSE) is usually treated in the real space in the textbook.However,it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast oscillation of the electron wave packets under the interaction of intense laser fields.Here we demonstrate that the TDSE can be efficiently solved in the momentum space.The high-order harmonic generation and above-threshold ionization spectra obtained by numerical solutions of TDSE in momentum space agree well with previous studies in real space,but significantly reducing the computation cost.
文摘Two interface capturing methods are studied for multi fluid flows, governed by the stiffened gas equation of state. The mixture type interface capturing algorithm uses a simple volume fraction model Euler equations written in a quasi conservative form, which is solved by a standard high resolution piecewise parabolic method (PPM) with multi fluid Riemann solver. The level set interface capturing method uses a narrow band ghost fluid method (GFM) with no numerical smearing. Several examples are presented and compared for one and two dimensions, which show the feasibility of the two methods applied to various multi fluid problems.
基金supported by the Natural ScienceFoundation of Shandong Province(ZR2021MA019)。
文摘In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.
文摘By conjugating features of combustion gas jetting flows of the solid-rocket and using mathematical methods, a numerical scheme is systematically derived based on Harten′s standard TVD scheme, which fits for the flow with high temperature, pressure and velocity. The rational calculation formula of pressure partial derivation is also given out. By using the chemical kinetics knowledge, problems of multi-component and finite rate chemical reaction contained in combustion gas of the rocket flow field are discussed. The method for solving the mass source term of chemical reaction is clarified. Taking 9 reaction equations with 12 components as an example and utilizing the established calculation program, the free jetting flow field of the rocket is simulated. Numerical results show the correctness of the numerical scheme.
文摘为研究颗粒阻尼器布置方案对多层结构减震性能的影响,制作了缩尺比为1/5的三层钢框架模型结构,进行了5条天然波下的地震模拟振动台试验,研究并联式单向单颗粒阻尼器(Parallel Single-dimensional Single Particle Damper,PSSPD)的减震控制效果。基于试验获得的模型自振频率、阻尼比等动力特性设计3种PSSPD布置方案,分析不同布置方案下模型结构的试验现象及位移和加速度响应。试验结果表明:PSSPD对结构响应峰值减震率可达到43.43%,均方根减震率可达到38.18%,其对多层结构具有良好的减震控制效果;PSSPD对结构均方根的平均减震效果要优于对峰值的平均减震效果;PSSPD布置方案对其减震效果影响显著,且其减震性能与本身参数、受控结构振动特性、地震动参数之间的耦合关系复杂。最后,建立PSSPD在任意布置方案下受控结构的力学模型,提出其数值分析流程。数值计算结果和试验结果在位移峰值及均方根方面具有良好的吻合度。
文摘Semisubmersible naval ships are versatile military crafts that combine the advantageous features of high-speed planing crafts and submarines.At-surface,these ships are designed to provide sufficient speed and maneuverability.Additionally,they can perform shallow dives,offering low visual and acoustic detectability.Therefore,the hydrodynamic design of a semisubmersible naval ship should address at-surface and submerged conditions.In this study,Numerical analyses were performed using a semisubmersible hull form to analyze its hydrodynamic features,including resistance,powering,and maneuvering.The simulations were conducted with Star CCM+version 2302,a commercial package program that solves URANS equations using the SST k-ωturbulence model.The flow analysis was divided into two parts:at-surface simulations and shallowly submerged simulations.At-surface simulations cover the resistance,powering,trim,and sinkage at transition and planing regimes,with corresponding Froude numbers ranging from 0.42 to 1.69.Shallowly submerged simulations were performed at seven different submergence depths,ranging from D/LOA=0.0635 to D/LOA=0.635,and at two different speeds with Froude numbers of 0.21 and 0.33.The behaviors of the hydrodynamic forces and pitching moment for different operation depths were comprehensively analyzed.The results of the numerical analyses provide valuable insights into the hydrodynamic performance of semisubmersible naval ships,highlighting the critical factors influencing their resistance,powering,and maneuvering capabilities in both at-surface and submerged conditions.
