Two computational cases that have analytic solutions are employed for studying the adaptive grid tech-nique based on the variational principle. The results show that for the computational case of traveling shock waves...Two computational cases that have analytic solutions are employed for studying the adaptive grid tech-nique based on the variational principle. The results show that for the computational case of traveling shock waves the weight function, with the 2nd-order derivation terms taken into consideration, can more effectively reduce the error than one with gradient terms. For the case of cyclonic frontogenesis, weight func-tions only related to the gradient are unable to enhance the computational accuracy while ones with the wind field and frontogenesis function taken into consideration can more reasonably arrange the grid. Com-pared with analytic solutions, the adaptive grid technique suggested in this paper can improve computational accuracy and it displays the prominent advantage of saving memory.展开更多
In this paper, integrating the Yangtze Estuary with the Hangzhou Bay, a 2-D velocity field model is established. In the model, fine self-adaptive grids are employed to adapt to the complicated coastal shape. The hydro...In this paper, integrating the Yangtze Estuary with the Hangzhou Bay, a 2-D velocity field model is established. In the model, fine self-adaptive grids are employed to adapt to the complicated coastal shape. The hydrodynamic equations satisfied by two contravariant components of velocity vector and surface elevation in non-orthogonal curvilinear coordinates are used. In each momentum equation the coefficients before the two partial derivatives of surface elevation with respect to variables of alternative direction coordinates have different orders of magnitude, i. e., the derivative with the larger coefficient may play a more important role than that with the smaller one. With this advantage, the ADI scheme can be easily employed. The hydrodynamic factors include tidal current, river runoff and wind-induced current. In terms of tidal current, seven main constituents in the area are considered in the open boundaries. The verifications of surface elevation process and current velocity process in the spring tide and in the neap tide show that the model can preferably reflect current fields in the area. Through the simulation of Lagrangian residual current fields in summer and in winter, the paths of the exchange of water and sediment between the Yangtze Estuary and the Hangzhou Bay are elementarily discussed.展开更多
The multi-resolution adaptive grids method is proposed to solve the problems of inefficiency in the previous grid-based methods,and it can be used in clouds simulation as well as the interactive simulation between obj...The multi-resolution adaptive grids method is proposed to solve the problems of inefficiency in the previous grid-based methods,and it can be used in clouds simulation as well as the interactive simulation between objects and clouds.Oriented bounding box(OBB)hierarchical trees of objects are established,and the resolutions of global and local grids can be selected automatically.The motion equations of fluid dynamics are simplified.Upwind difference is applied to ensure the stability of the simulation process during the discrete process of partial differential equations.To solve the speed problem of existed phase functions,the improved phase function is applied to the illumination calculation of clouds.Experimental results show that the proposed methods can promote the simulation efficiency and meet the need for the simulation of large-scale clouds scene.Real-time rendering of clouds and the interaction between clouds and objects have been realized without preprocessing stage.展开更多
The dynamics of the Liesegang type pattern formation is investigated in a centrally symmetric two-dimensional setup.According to the observations in real experiments,the qualitative change of the dynamics is exhibited...The dynamics of the Liesegang type pattern formation is investigated in a centrally symmetric two-dimensional setup.According to the observations in real experiments,the qualitative change of the dynamics is exhibited for slightly different initial conditions.Two kinds of chemical mechanisms are studied;in both cases the pattern formation is described using a phase separation model including the CahnHilliard equations.For the numerical simulations we make use of an adaptive grid PDE method,which successfully deals with the computationally critical cases such as steep gradients in the concentration distribution and investigation of long time behavior.The numerical simulations show a good agreement with the real experiments.展开更多
For the large deformation of the flexible body may cause the fluid grid distortion,which will make the numerical calculation tedious,even to end,the numerical simulation of the flexible body coupling with the fluid is...For the large deformation of the flexible body may cause the fluid grid distortion,which will make the numerical calculation tedious,even to end,the numerical simulation of the flexible body coupling with the fluid is always a tough problem.In this paper,the flexible body is under two kinds of constrained conditions and the ratio of length-diameter is 1:30.The Reynolds number of the airflow is 513,belonging to the area of low Reynolds number.The control equations of the coupling of flexible body with airflow are built and the adaptive grid control method is adopted to conduct the three-dimensional numerical simulation of the movement of the flexible body.The numerical results show that it is possible to simulate the characteristics of the flexible body's movement in the low Reynolds number airflow when the appropriate control equations are modeled and suitable equation-solving method is adopted.Unconstrained flexible body would turn over forward along the airflow's diffusion direction,while constrained flexible body in the flow field will make periodic rotation motion along the axis of the flexible body,and the bending deformation is more obvious than that of unconstrained flexible body.The preliminary three-dimensional numerical simulation can provide references for further research on the characteristics of the yam movement in high Reynolds number airflow.展开更多
A new method is presented to study the function projective lag synchronization(FPLS) of chaotic systems via adaptive-impulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are...A new method is presented to study the function projective lag synchronization(FPLS) of chaotic systems via adaptive-impulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are designed. Based on the Lyapunov stability theory and the impulsive control technology, some effective sufficient conditions are derived to ensure the drive system and the response system can be rapidly lag synchronized up to the given scaling function matrix. Numerical simulations are presented to verify the effectiveness and the feasibility of the analytical results.展开更多
Classical continuum mechanics which leads to a local continuum model,encounters challenges when the discontinuity appears,while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a ...Classical continuum mechanics which leads to a local continuum model,encounters challenges when the discontinuity appears,while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost.A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages.This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials.Then this hybrid local/nonlocal continuum model is applied to fracture simulation.Some numerical examples like a plate with a hole,Brazilian disk,notched plate and beam,are performed for verification and validation.In addition,a peridynamic software is introduced,which was recently developed for the simulation of the hybrid local/nonlocal continuum model.展开更多
The flows behind the base of a generic rocket, at both hypersonic and subsonic flow conditions, are numerically studied. The main concerns are addressed to the evaluation of turbulence models and the using of grid ada...The flows behind the base of a generic rocket, at both hypersonic and subsonic flow conditions, are numerically studied. The main concerns are addressed to the evaluation of turbulence models and the using of grid adaptation techniques. The investigation focuses on two configurations, related to hypersonic and subsonic experiments. The applicability tests of different turbu- lence models are conducted on the level of two-equation models calculating the steady state solution of the Reynolds-averaged Navier-Stokes（RANS） equations. All used models, the original Wilcox k-co, the Menter shear-stress transport （SST） and the ex- plicit algebraic Reynolds stress model（EARSM） formulation, predict an asymmetric base flow in both cases caused by the support of the models. A comparison with preliminary experimental results indicates a preference for the SST and EARSM results over the results from the older k-co model. Sensitivity studies show no significant influence of the grid topology or the location of the laminar to turbulent transition on the base flow field, but a strong influence of even small angles of attack is reported from the related experiments.展开更多
基金Acknowledgments. The research report has been supported jointly by the National Natural Science Foundation of China under Grant Nos.40075024 and 49945009, and by the National Key Basic Research and Development Proj-ect under Grant No. G1998040911.
文摘Two computational cases that have analytic solutions are employed for studying the adaptive grid tech-nique based on the variational principle. The results show that for the computational case of traveling shock waves the weight function, with the 2nd-order derivation terms taken into consideration, can more effectively reduce the error than one with gradient terms. For the case of cyclonic frontogenesis, weight func-tions only related to the gradient are unable to enhance the computational accuracy while ones with the wind field and frontogenesis function taken into consideration can more reasonably arrange the grid. Com-pared with analytic solutions, the adaptive grid technique suggested in this paper can improve computational accuracy and it displays the prominent advantage of saving memory.
基金National Natural Science Foundation of China under contract No.49776279National Excellent Youth Foundation of China under contract No.49825161
文摘In this paper, integrating the Yangtze Estuary with the Hangzhou Bay, a 2-D velocity field model is established. In the model, fine self-adaptive grids are employed to adapt to the complicated coastal shape. The hydrodynamic equations satisfied by two contravariant components of velocity vector and surface elevation in non-orthogonal curvilinear coordinates are used. In each momentum equation the coefficients before the two partial derivatives of surface elevation with respect to variables of alternative direction coordinates have different orders of magnitude, i. e., the derivative with the larger coefficient may play a more important role than that with the smaller one. With this advantage, the ADI scheme can be easily employed. The hydrodynamic factors include tidal current, river runoff and wind-induced current. In terms of tidal current, seven main constituents in the area are considered in the open boundaries. The verifications of surface elevation process and current velocity process in the spring tide and in the neap tide show that the model can preferably reflect current fields in the area. Through the simulation of Lagrangian residual current fields in summer and in winter, the paths of the exchange of water and sediment between the Yangtze Estuary and the Hangzhou Bay are elementarily discussed.
基金supported by the National Natural Science Foundation of China(No.61102167)
文摘The multi-resolution adaptive grids method is proposed to solve the problems of inefficiency in the previous grid-based methods,and it can be used in clouds simulation as well as the interactive simulation between objects and clouds.Oriented bounding box(OBB)hierarchical trees of objects are established,and the resolutions of global and local grids can be selected automatically.The motion equations of fluid dynamics are simplified.Upwind difference is applied to ensure the stability of the simulation process during the discrete process of partial differential equations.To solve the speed problem of existed phase functions,the improved phase function is applied to the illumination calculation of clouds.Experimental results show that the proposed methods can promote the simulation efficiency and meet the need for the simulation of large-scale clouds scene.Real-time rendering of clouds and the interaction between clouds and objects have been realized without preprocessing stage.
基金support from the Dutch BSIK-project BRICKSthe financial support of the Bolyai Research Fellow-ship,the Hungarian Scientific Research Fund(OTKA K68253 and K81933)the European Union and the European Social Fund(TAMOP 4.2.1./B-09/KMR-2010-0003).
文摘The dynamics of the Liesegang type pattern formation is investigated in a centrally symmetric two-dimensional setup.According to the observations in real experiments,the qualitative change of the dynamics is exhibited for slightly different initial conditions.Two kinds of chemical mechanisms are studied;in both cases the pattern formation is described using a phase separation model including the CahnHilliard equations.For the numerical simulations we make use of an adaptive grid PDE method,which successfully deals with the computationally critical cases such as steep gradients in the concentration distribution and investigation of long time behavior.The numerical simulations show a good agreement with the real experiments.
基金supported by Zhejiang Provincial Natural Science Foundation under Grant No.LZ14E050004,LQ12A02002 etc
文摘For the large deformation of the flexible body may cause the fluid grid distortion,which will make the numerical calculation tedious,even to end,the numerical simulation of the flexible body coupling with the fluid is always a tough problem.In this paper,the flexible body is under two kinds of constrained conditions and the ratio of length-diameter is 1:30.The Reynolds number of the airflow is 513,belonging to the area of low Reynolds number.The control equations of the coupling of flexible body with airflow are built and the adaptive grid control method is adopted to conduct the three-dimensional numerical simulation of the movement of the flexible body.The numerical results show that it is possible to simulate the characteristics of the flexible body's movement in the low Reynolds number airflow when the appropriate control equations are modeled and suitable equation-solving method is adopted.Unconstrained flexible body would turn over forward along the airflow's diffusion direction,while constrained flexible body in the flow field will make periodic rotation motion along the axis of the flexible body,and the bending deformation is more obvious than that of unconstrained flexible body.The preliminary three-dimensional numerical simulation can provide references for further research on the characteristics of the yam movement in high Reynolds number airflow.
基金supported by National Natural Science Foundation of China (Nos. 41571417 and U1604145)Science and Technology Foundation of Henan Province of China (No. 152102210048)+3 种基金Foundation and Frontier Project of Henan Province of China (No. 162300410196)China Postdoctoral Science Foundation (No. 2016M602235)Natural Science Foundation of Educational Committee of Henan Province of China (No. 14A413015)Research Foundation of Henan University (No. xxjc20140006)
文摘A new method is presented to study the function projective lag synchronization(FPLS) of chaotic systems via adaptive-impulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are designed. Based on the Lyapunov stability theory and the impulsive control technology, some effective sufficient conditions are derived to ensure the drive system and the response system can be rapidly lag synchronized up to the given scaling function matrix. Numerical simulations are presented to verify the effectiveness and the feasibility of the analytical results.
基金The authors gratefully acknowledge the financial support received from KAUST baseline,the National Natural Science Foundation(11872016)the Fundamental Research Funds of Dalian University of Technology(Grant No.DUT17RC(3)092)for the completion of this work.
文摘Classical continuum mechanics which leads to a local continuum model,encounters challenges when the discontinuity appears,while peridynamics that falls into the category of nonlocal continuum mechanics suffers from a high computational cost.A hybrid model coupling classical continuum mechanics with peridynamics can avoid both disadvantages.This paper describes the hybrid model and its adaptive coupling approach which dynamically updates the coupling domains according to crack propagations for brittle materials.Then this hybrid local/nonlocal continuum model is applied to fracture simulation.Some numerical examples like a plate with a hole,Brazilian disk,notched plate and beam,are performed for verification and validation.In addition,a peridynamic software is introduced,which was recently developed for the simulation of the hybrid local/nonlocal continuum model.
基金German Research Foundation (Deutsche Forschungs-gemeinschaft-DFG) Sonderforschungsbereich Transregio 40
文摘The flows behind the base of a generic rocket, at both hypersonic and subsonic flow conditions, are numerically studied. The main concerns are addressed to the evaluation of turbulence models and the using of grid adaptation techniques. The investigation focuses on two configurations, related to hypersonic and subsonic experiments. The applicability tests of different turbu- lence models are conducted on the level of two-equation models calculating the steady state solution of the Reynolds-averaged Navier-Stokes（RANS） equations. All used models, the original Wilcox k-co, the Menter shear-stress transport （SST） and the ex- plicit algebraic Reynolds stress model（EARSM） formulation, predict an asymmetric base flow in both cases caused by the support of the models. A comparison with preliminary experimental results indicates a preference for the SST and EARSM results over the results from the older k-co model. Sensitivity studies show no significant influence of the grid topology or the location of the laminar to turbulent transition on the base flow field, but a strong influence of even small angles of attack is reported from the related experiments.
