By comparing the energy spectrum and total kinetic energy, the effects of numerical errors （which arise from aliasing and discretization errors）, subgrid-scale （SGS） models, and their interactions on direct numeri...By comparing the energy spectrum and total kinetic energy, the effects of numerical errors （which arise from aliasing and discretization errors）, subgrid-scale （SGS） models, and their interactions on direct numerical simulation （DNS） and large eddy simulation （LES） are investigated, The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Pade compact difference schemes are studied. The truncated Navier-Stokes （TNS） equation model with Pade discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.展开更多
The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smoo...The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.展开更多
On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time - dependent numerical model for the water wave propagation has been established combined with diffe...On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time - dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin＇s model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin＇s model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin＇ s model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real - time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research an d engineering applications about the wave propagation in a biggish area.展开更多
A feedforward compensation naethod of the motion errors of NC machine tools imple- mented with software is proposed , with which the motion errors can be compensated whithout changing the original computer control sys...A feedforward compensation naethod of the motion errors of NC machine tools imple- mented with software is proposed , with which the motion errors can be compensated whithout changing the original computer control systems of the NC machine tools. The experimental results show that the circular interpolation profile machining errors decrease by a factor of 2/3 after com- pensated.展开更多
This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not ...This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration （iterative） and the operator-splitting （non-iterative） is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom （SDOF） cantilever column with replaceable steel coupons that provides repeatable highly- nonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1：2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model ofa 1：2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.展开更多
The frictional properties of micro bearings have strong influence on the performance of the whole system because of tiny scale of micro-electromechanical system (MEMS). To develop micro bearings with low friction,it i...The frictional properties of micro bearings have strong influence on the performance of the whole system because of tiny scale of micro-electromechanical system (MEMS). To develop micro bearings with low friction,it is important to evaluate the friction behaviors on the micro bearing. The testing system and the principle to evaluate the tribological performance of micromachining work-pieces under the load of mill Newton scale is introduced in paper "A new approach to measure the friction coefficient of micro journal bearings" of Yao et al,. But as the tribological force is faint in micro scale, the measured force is influenced a lot by the testing error. As the equation of that of Yao’s paper is very sensitive to the measured force, the tested result is influenced remarkably by testing error. So it is hard to get precision result. To solve this problem, the test system with new compensation method is introduced to precisely evaluate tribological performance under mill scale. The new metrology method is developed by means of the error compensation from two sets of testing data. The data are the force collected respectively when the friction counterparts rotate in CW(clockwise) and CCW(counter-clockwise) direction. So we deduce the equation of friction coefficient respctively on the condition of journal running in CCW and CW direction. As condition of measuring those two friciton coefficients are alike except the running direction of journal, and then the friction coefficient should be the same because this difference of direction has no influence on the fricition coefficients. Considering this, we unite the both equation, make the data measured in different subtract each other in the equation, and then a new equation can be gotten. This new equation enhances the metrology precision of friction coefficient theoretically thanks to the counteracting of error values in the equation. Using this method we testing the friction of high speed steel journal with hard alloy bearing. The result shows the new compensation method has better precision and repetition than CW and CCW method thanks to the error resistance.展开更多
Based on the atmospheric analogy principle, the inverse problem that the information of historical analogue data is utilized to estimate model errors is put forward and a method of analogue correction of errors （ACE...Based on the atmospheric analogy principle, the inverse problem that the information of historical analogue data is utilized to estimate model errors is put forward and a method of analogue correction of errors （ACE） of model is developed in this paper. The ACE can combine effectively statistical and dynamical methods, and need not change the current numerical prediction models. The new method not only adequately utilizes dynamical achievements but also can reasonably absorb the information of a great many analogues in historical data in order to reduce model errors and improve forecast skill. Purthermore, the ACE may identify specific historical data for the solution of the inverse problem in terms of the particularity of current forecast. The qualitative analyses show that the ACE is theoretically equivalent to the principle of the previous analogue-dynamical model, but need not rebuild the complicated analogue-deviation model, so has better feasibility and operational foreground. Moreover, under the ideal situations, when numerical models or historical analogues are perfect, the forecast of the ACE would transform into the forecast of dynamical or statistical method, respectively.展开更多
Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combi...Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.展开更多
We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems： additional edge singularities are known to develop in that case. This pa...We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems： additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered： the Laplace equation in free space, the linear elasticity equation in free space, and in half space.展开更多
The article is to report some results of numerical experiments on the error growth and the atmospheric predictability Experiments with two-level global baroclinic primitive equation spectral model have main results as...The article is to report some results of numerical experiments on the error growth and the atmospheric predictability Experiments with two-level global baroclinic primitive equation spectral model have main results as follows.The magnitude of initial errors directly affects the error growth,but its distribution form has little effect on the growth.The loss of predictability resulting from small-scale error is much greater than that from large-scale error.The small-scale error rapidly grows and is transferred to the large-scale error by interaction between different scale waves,which stimulates the growth of error for the whole system Orographic forcing restrains planetary-scale error(wavenumbers 0—3)but enhances the small-scale error (wavenumbers 8 or greater).Hence,orographic effects on the error growth closely depend on the characteris- tic scale of initial errors,and there may be a critical wavenumber between 4 and 7.The error growth is great- er in Northern Hemisphere than in Southern Hemisphere if initial errors are the same.In the end we give some discussions about model,initialization scheme,etc.,to improve model prediction.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10502029)the Scientific Research Foundation for Returned Overseas Chinese Scholars of Ministry of Education of China
文摘By comparing the energy spectrum and total kinetic energy, the effects of numerical errors （which arise from aliasing and discretization errors）, subgrid-scale （SGS） models, and their interactions on direct numerical simulation （DNS） and large eddy simulation （LES） are investigated, The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Pade compact difference schemes are studied. The truncated Navier-Stokes （TNS） equation model with Pade discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.
基金Supported by the National Natural Science Foundation of China(42230606)14th Five-Year Plan Basic Research Program of Institute of Atmospheric Physics,Chinese Academy of Sciences(E268081801)National Key Research and Development Program of China(2017YFA0603901)。
文摘The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.
文摘On the basis of the previous studies, the simplest hyperbolic mild-slope equation has been gained and the linear time - dependent numerical model for the water wave propagation has been established combined with different boundary conditions. Through computing the effective surface displacement and transforming into the real transient wave motion, related wave factors will be calculated. Compared with Lin＇s model, analysis shows that calculation stability of the present model is enhanced efficiently, because the truncation errors of this model are only contributed by the dissipation terms, but those of Lin＇s model are induced by the convection terms, dissipation terms and source terms. The tests show that the present model succeeds the merit in Lin＇ s model and the computational program is simpler, the computational time is shorter, and the computational stability is enhanced efficiently. The present model has the capability of simulating transient wave motion by correctly predicting at the speed of wave propagation, which is important for the real - time forecast of the arrival time of surface waves generated in the deep sea. The model is validated against analytical solution for wave diffraction and experimental data for combined wave refraction and diffraction over a submerged elliptic shoal on a slope. Good agreements are obtained. The model can be applied to the theory research an d engineering applications about the wave propagation in a biggish area.
文摘A feedforward compensation naethod of the motion errors of NC machine tools imple- mented with software is proposed , with which the motion errors can be compensated whithout changing the original computer control systems of the NC machine tools. The experimental results show that the circular interpolation profile machining errors decrease by a factor of 2/3 after com- pensated.
基金National Science Foundation(NSF)under grant No.CMMI-0748111
文摘This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration （iterative） and the operator-splitting （non-iterative） is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom （SDOF） cantilever column with replaceable steel coupons that provides repeatable highly- nonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1：2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model ofa 1：2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.
文摘The frictional properties of micro bearings have strong influence on the performance of the whole system because of tiny scale of micro-electromechanical system (MEMS). To develop micro bearings with low friction,it is important to evaluate the friction behaviors on the micro bearing. The testing system and the principle to evaluate the tribological performance of micromachining work-pieces under the load of mill Newton scale is introduced in paper "A new approach to measure the friction coefficient of micro journal bearings" of Yao et al,. But as the tribological force is faint in micro scale, the measured force is influenced a lot by the testing error. As the equation of that of Yao’s paper is very sensitive to the measured force, the tested result is influenced remarkably by testing error. So it is hard to get precision result. To solve this problem, the test system with new compensation method is introduced to precisely evaluate tribological performance under mill scale. The new metrology method is developed by means of the error compensation from two sets of testing data. The data are the force collected respectively when the friction counterparts rotate in CW(clockwise) and CCW(counter-clockwise) direction. So we deduce the equation of friction coefficient respctively on the condition of journal running in CCW and CW direction. As condition of measuring those two friciton coefficients are alike except the running direction of journal, and then the friction coefficient should be the same because this difference of direction has no influence on the fricition coefficients. Considering this, we unite the both equation, make the data measured in different subtract each other in the equation, and then a new equation can be gotten. This new equation enhances the metrology precision of friction coefficient theoretically thanks to the counteracting of error values in the equation. Using this method we testing the friction of high speed steel journal with hard alloy bearing. The result shows the new compensation method has better precision and repetition than CW and CCW method thanks to the error resistance.
基金Supported jointly by the National Natural Science Foundation of China under Grant Nos. 40233031, 40575036 and 40675039.
文摘Based on the atmospheric analogy principle, the inverse problem that the information of historical analogue data is utilized to estimate model errors is put forward and a method of analogue correction of errors （ACE） of model is developed in this paper. The ACE can combine effectively statistical and dynamical methods, and need not change the current numerical prediction models. The new method not only adequately utilizes dynamical achievements but also can reasonably absorb the information of a great many analogues in historical data in order to reduce model errors and improve forecast skill. Purthermore, the ACE may identify specific historical data for the solution of the inverse problem in terms of the particularity of current forecast. The qualitative analyses show that the ACE is theoretically equivalent to the principle of the previous analogue-dynamical model, but need not rebuild the complicated analogue-deviation model, so has better feasibility and operational foreground. Moreover, under the ideal situations, when numerical models or historical analogues are perfect, the forecast of the ACE would transform into the forecast of dynamical or statistical method, respectively.
基金Supported by State Major Key Project for Basic Researches and the National Natural Science Foundation of China.
文摘Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.
文摘We present in this paper a numerical method for hypersingular boundary integral equations. This method was developed for planar crack problems： additional edge singularities are known to develop in that case. This paper includes a rigorous error analysis proving the convergence of our numerical scheme. Three types of examples are covered： the Laplace equation in free space, the linear elasticity equation in free space, and in half space.
文摘The article is to report some results of numerical experiments on the error growth and the atmospheric predictability Experiments with two-level global baroclinic primitive equation spectral model have main results as follows.The magnitude of initial errors directly affects the error growth,but its distribution form has little effect on the growth.The loss of predictability resulting from small-scale error is much greater than that from large-scale error.The small-scale error rapidly grows and is transferred to the large-scale error by interaction between different scale waves,which stimulates the growth of error for the whole system Orographic forcing restrains planetary-scale error(wavenumbers 0—3)but enhances the small-scale error (wavenumbers 8 or greater).Hence,orographic effects on the error growth closely depend on the characteris- tic scale of initial errors,and there may be a critical wavenumber between 4 and 7.The error growth is great- er in Northern Hemisphere than in Southern Hemisphere if initial errors are the same.In the end we give some discussions about model,initialization scheme,etc.,to improve model prediction.
