An implicit electrostatic particle-in-cell/Monte Carlo （PIC/MC） algorithm is developed for the magnetized discharging device simulation. The inductive driving force can be considered. The direct implicit PIC algorit...An implicit electrostatic particle-in-cell/Monte Carlo （PIC/MC） algorithm is developed for the magnetized discharging device simulation. The inductive driving force can be considered. The direct implicit PIC algorithm （DIPIC） and energy conservation scheme are applied together and the grid heating can be eliminated in most cases. A tensor-susceptibility Poisson equation is constructed. Its discrete form is made up by a hybrid scheme in one-dimensional （1D） and two- dimensional （2D） cylindrical systems. A semi-coarsening multigrid method is used to solve the discrete system. The algorithm is applied to simulate the cylindrical magnetized target fusion （MTF） pre-ionization process and get qualitatively correct results. The potential application of the algorithm is discussed briefly.展开更多
The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics.However,it is time-consuming to obtain the future electromagnetic field in such a method since the field equatio...The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics.However,it is time-consuming to obtain the future electromagnetic field in such a method since the field equations contain time-dependent matrix coefficients.In this work,we propose to explicitly push particles and obtain the future electromagnetic field based on the information about the particles in the future.The new method retains the form of implicit particle pusher,but the future field is obtained by solving the traditional explicit equation.Several numerical experiments,including the motion of charged particle in electromagnetic field,plasma sheath,and free diffusion of plasma into vacuum,are implemented to evaluate the performance of the method.The results demonstrate that the proposed method can suppress finite-grid-instability resulting from the coarse spatial resolution in electron Debye length through the strong damping of high-frequency plasma oscillation,while accurately describe low-frequency plasma phenomena,with the price of losing the numerical stability at large time-step.We believe that this work is helpful for people to research the bounded plasma by using particle-in-cell simulations.展开更多
We report the results of protein folding （219M, C34, N36, 2KES, 2KHK） by the method of accelerated molecular dynamics （aMD） at room temperature with the implicit solvent model. Starting from the linear structures,...We report the results of protein folding （219M, C34, N36, 2KES, 2KHK） by the method of accelerated molecular dynamics （aMD） at room temperature with the implicit solvent model. Starting from the linear structures, these proteins successfully fold to the native structure in a lO0-ns aMD simulation. In contrast, they are failed under the traditional MD simulation in the same simulation time. Then we find that the lowest root mean square deviations of helix structures from the native structures are 0.36 A, 0.63 A, 0.52 A, 1.1 A and 0.78 A. What is more, native contacts, cluster and free energy analyses show that the results of the aMD method are in accordance with the experiment very well. All analyses show that the aMD can accelerate the simulation process, thus we may apply it to the field of computer aided drug designs.展开更多
The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large...The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation （ILES） is app- lied to analyze the three-dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic conditions, which were experimentally tested at the high speed cavitation tunnel of the l^cole Polytechnique F6d＆ale de Lausanne （EPFL）, clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasona- bly well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.展开更多
The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in ma...The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.展开更多
Steel sets are widely used in tunnels with unfavorable geological conditions.Such steel sets always have small dimensions and are densely installed on the excavation surface,which is why performing nonlinear analysis ...Steel sets are widely used in tunnels with unfavorable geological conditions.Such steel sets always have small dimensions and are densely installed on the excavation surface,which is why performing nonlinear analysis on steel sets in actual engineering is a challenging task.Therefore,an implicit nonlinear finite element method(FEM)for steel sets in tunnels was proposed.First,considering the mechanical characteristics of the steel set,a mathematical model of the steel set was proposed,which can accurately reflect the arch effect of the steel set.Then,the stress-strain relationship of the steel set was divided into the linear elastic stage,the first yield platform stage,the nonlinear hardening stage,and the second yield platform stage.In combination with the mixed hardening model,a nonlinear mechanical model of the steel set was established,and its rationality was verified by a thick aluminum ring example.Thirdly,for the convenience of engineering applications,steel sets were implied into rock elements,and their elastoplastic stiffness was superimposed into rock elements to reflect their supporting action.Furthermore,a stress update algorithm for the steel sets in the nonlinear iterative process and a method to simulate their fracture failure were provided.These models were incorporated into a self-developed FEM program to conduct nonlinear analysis for steel sets in tunnels.Finally,the proposed method was applied in a cross-fault hydraulic tunnel.The results proved its rationality,and some conclusions of interest were obtained.This method does not need to establish a complex solid model for steel sets,has no influence on the meshes of rock elements,and can simulate the whole process of steel sets from the linear elastic stage to the nonlinear hardening stage and finally to the fracture failure stage.Thus,it may be a convenient method of simulating steel sets in tunnels.展开更多
The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil productio...The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil production at a minimum cost, and represents the future direction of oil fields. This paper discusses the core of the smart field theory, mainly the real-time optimization method of the injection-production rate of water-oil wells in a complex oil-gas filtration system. Computing speed is considered as the primary prerequisite because this research depends very much on reservoir numerical simulations and each simulation may take several hours or even days. An adjoint gradient method of the maximum theory is chosen for the solution of the optimal control variables. Conven-tional solving method of the maximum principle requires two solutions of time series： the forward reservoir simulation and the backward adjoint gradient calculation. In this paper, the two processes are combined together and a fully implicit reservoir simulator is developed. The matrixes of the adjoint equation are directly obtained from the fully implicit reservoir simulation, which accelera-tes the optimization solution and enhances the efficiency of the solving model. Meanwhile, a gradient projection algorithm combined with the maximum theory is used to constrain the parameters in the oil field development, which make it possible for the method to be applied to the water flooding optimization in a real oil field. The above theory is tested in several reservoir cases and it is shown that a better development effect of the oil field can be achieved.展开更多
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomia...The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials,modified to accommodate a C~0-continuous expansion. Computationally and theoretically, by increasing the polynomial order p,high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.展开更多
A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broad...A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11275007,11105057,11175023,and 11275039)One of the author(Wang H Y)is supported by Program for Liaoning Excellent Talents in University(Grant No.LJQ2012098)
文摘An implicit electrostatic particle-in-cell/Monte Carlo （PIC/MC） algorithm is developed for the magnetized discharging device simulation. The inductive driving force can be considered. The direct implicit PIC algorithm （DIPIC） and energy conservation scheme are applied together and the grid heating can be eliminated in most cases. A tensor-susceptibility Poisson equation is constructed. Its discrete form is made up by a hybrid scheme in one-dimensional （1D） and two- dimensional （2D） cylindrical systems. A semi-coarsening multigrid method is used to solve the discrete system. The algorithm is applied to simulate the cylindrical magnetized target fusion （MTF） pre-ionization process and get qualitatively correct results. The potential application of the algorithm is discussed briefly.
基金Project supported by the National Key Research and Development Program of China (Grant No.2022YFE03050001)partly by the National Natural Science Foundation of China (Grant No.12175160)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)。
文摘The direct implicit particle-in-cell is a powerful kinetic method for researching plasma characteristics.However,it is time-consuming to obtain the future electromagnetic field in such a method since the field equations contain time-dependent matrix coefficients.In this work,we propose to explicitly push particles and obtain the future electromagnetic field based on the information about the particles in the future.The new method retains the form of implicit particle pusher,but the future field is obtained by solving the traditional explicit equation.Several numerical experiments,including the motion of charged particle in electromagnetic field,plasma sheath,and free diffusion of plasma into vacuum,are implemented to evaluate the performance of the method.The results demonstrate that the proposed method can suppress finite-grid-instability resulting from the coarse spatial resolution in electron Debye length through the strong damping of high-frequency plasma oscillation,while accurately describe low-frequency plasma phenomena,with the price of losing the numerical stability at large time-step.We believe that this work is helpful for people to research the bounded plasma by using particle-in-cell simulations.
基金Supported by the National Natural Science Foundation of China under Grant Nos 31200545,11274206 and 11574184
文摘We report the results of protein folding （219M, C34, N36, 2KES, 2KHK） by the method of accelerated molecular dynamics （aMD） at room temperature with the implicit solvent model. Starting from the linear structures, these proteins successfully fold to the native structure in a lO0-ns aMD simulation. In contrast, they are failed under the traditional MD simulation in the same simulation time. Then we find that the lowest root mean square deviations of helix structures from the native structures are 0.36 A, 0.63 A, 0.52 A, 1.1 A and 0.78 A. What is more, native contacts, cluster and free energy analyses show that the results of the aMD method are in accordance with the experiment very well. All analyses show that the aMD can accelerate the simulation process, thus we may apply it to the field of computer aided drug designs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51306018,51536008 and 51179091)
文摘The present paper focuses on the erosive cavitation behavior around a plane convex hydrofoil. The Zwart-Gerber-Belamri cavitation model is implemented in a library form to be used with the OpenFOAM. The implicit large eddy simulation （ILES） is app- lied to analyze the three-dimensional unsteady cavitating flow around a plane convex hydrofoil. The numerical results in the cases under the hydrodynamic conditions, which were experimentally tested at the high speed cavitation tunnel of the l^cole Polytechnique F6d＆ale de Lausanne （EPFL）, clearly show the sheet cavitation development, the shedding and the collapse of vapor clouds. It is noted that the cavitation evolutions including the maximum vapor length, the detachment and the oscillation frequency, are captured fairly well. Furthermore, the pressure pulses due to the cavitation development as well as the complex vortex structures are reasona- bly well predicted. Consequently, it may be concluded that the present numerical method can be used to investigate the unsteady cavitation around hydrofoils with a satisfactory accuracy.
基金the financial support provided by the Defense Acquisition Program Administration(DAPA)under Grant UD200046CD(Data-driven Flow Modeling Research Laboratory)the Korea Research Institute for defense Technology planning and advancement(KRIT)under Grant KRIT-CT-22-030(Reusable Unmanned Space Vehicle Research Center,2023)supported by the program of the National Research Foundation of Korea(NRF-2021R1A2C2008348).
文摘The present study develops implicit physical domain-based discontinuous Galerkin(DG)methods for efficient scale-resolving simulations on mixed-curved meshes.Implicit methods are essential to handle stiff systems in many scale-resolving simulations of interests in computational science and engineering.The physical domain-based DGmethod can achieve high-order accuracy using the optimal bases set and preserve the required accuracy on non-affinemeshes.When using the quadraturebased DG method,these advantages are overshadowed by severe computational costs on mixed-curved meshes,making implicit scale-resolving simulations unaffordable.To address this issue,the quadrature-free direct reconstruction method(DRM)is extended to the implicit DG method.In this approach,the generalized reconstruction approximates non-linear flux functions directly in the physical domain,making the computing-intensive numerical integrations precomputable at a preprocessing step.The DRM operator is applied to the residual computation in the matrix-free method.The DRM operator can be further extended to the system matrix computation for the matrix-explicit Krylov subspace method and preconditioning.Finally,the A-stable Rosenbrock-type Runge–Kutta methods are adopted to achieve high-order accuracy in time.Extensive verification and validation from the manufactured solution to implicit large eddy simulations are conducted.The computed results confirm that the proposed method significantly improves computational efficiency compared to the quadrature-based method while accurately resolving detailed unsteady flow features that are hardly captured by scale-modeled simulations.
基金supported by the National Natural Science Foundation of China(Grant No.52079097)。
文摘Steel sets are widely used in tunnels with unfavorable geological conditions.Such steel sets always have small dimensions and are densely installed on the excavation surface,which is why performing nonlinear analysis on steel sets in actual engineering is a challenging task.Therefore,an implicit nonlinear finite element method(FEM)for steel sets in tunnels was proposed.First,considering the mechanical characteristics of the steel set,a mathematical model of the steel set was proposed,which can accurately reflect the arch effect of the steel set.Then,the stress-strain relationship of the steel set was divided into the linear elastic stage,the first yield platform stage,the nonlinear hardening stage,and the second yield platform stage.In combination with the mixed hardening model,a nonlinear mechanical model of the steel set was established,and its rationality was verified by a thick aluminum ring example.Thirdly,for the convenience of engineering applications,steel sets were implied into rock elements,and their elastoplastic stiffness was superimposed into rock elements to reflect their supporting action.Furthermore,a stress update algorithm for the steel sets in the nonlinear iterative process and a method to simulate their fracture failure were provided.These models were incorporated into a self-developed FEM program to conduct nonlinear analysis for steel sets in tunnels.Finally,the proposed method was applied in a cross-fault hydraulic tunnel.The results proved its rationality,and some conclusions of interest were obtained.This method does not need to establish a complex solid model for steel sets,has no influence on the meshes of rock elements,and can simulate the whole process of steel sets from the linear elastic stage to the nonlinear hardening stage and finally to the fracture failure stage.Thus,it may be a convenient method of simulating steel sets in tunnels.
基金Project supported by the China Important National Science and Technology Specific Projects(Grant No.2011ZX05024-002-008)the Fundamental Research Funds for the Central Universities(Grant No.13CX02053A)the Changjiang Scholars and Innovative Reserch Team in University(Grant No.IRT1294)
文摘The oil recovery enhancement is a major technical issue in the development of oil and gas fields. The smart oil field is an effective way to deal with the issue. It can achieve the maximum profits in the oil production at a minimum cost, and represents the future direction of oil fields. This paper discusses the core of the smart field theory, mainly the real-time optimization method of the injection-production rate of water-oil wells in a complex oil-gas filtration system. Computing speed is considered as the primary prerequisite because this research depends very much on reservoir numerical simulations and each simulation may take several hours or even days. An adjoint gradient method of the maximum theory is chosen for the solution of the optimal control variables. Conven-tional solving method of the maximum principle requires two solutions of time series： the forward reservoir simulation and the backward adjoint gradient calculation. In this paper, the two processes are combined together and a fully implicit reservoir simulator is developed. The matrixes of the adjoint equation are directly obtained from the fully implicit reservoir simulation, which accelera-tes the optimization solution and enhances the efficiency of the solving model. Meanwhile, a gradient projection algorithm combined with the maximum theory is used to constrain the parameters in the oil field development, which make it possible for the method to be applied to the water flooding optimization in a real oil field. The above theory is tested in several reservoir cases and it is shown that a better development effect of the oil field can be achieved.
文摘The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials,modified to accommodate a C~0-continuous expansion. Computationally and theoretically, by increasing the polynomial order p,high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
基金supported by the National Natural Science Foundation of China(Grant No.11402016)the Fundamental Research Funds for the Central Universities(Grant Nos.50100002014105020&50100002015105033)
文摘A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.
