The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solut...The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.展开更多
This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we stu...This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.展开更多
This paper presents an Operator -Splitting Method (OSM) for the solution of the universal Reynolds equation. Jakoobsson-Floberg-Olsson (JFO) pressure conditions were incorporated for the study of cavitation in a liqui...This paper presents an Operator -Splitting Method (OSM) for the solution of the universal Reynolds equation. Jakoobsson-Floberg-Olsson (JFO) pressure conditions were incorporated for the study of cavitation in a liquid-lubricated journal bearings. Shear flow component of the oil film was first solved by a modified upwind finite difference method. The solution of the pressure gradient flow component was completed by the Galerkin finite element method. Present OSM solutions for a slider bearing are in agreement with Elord's results. OSM was then applied to herringbone grooved journal bearing in this work. The film pressure, cavitation areas, load capacity and attitude angle were obtained with JFO pressure conditions. The calculated load capacities are in agreement with Hirs's experimental data. A comparison of the present results and those predicted by the Reynolds pressure conditions shows some differences. The numerical results indicate that the load capacity and the critical mass of journal (linear stability indicator) are higher, and the attitude angle is lower than those predicted by Reynolds pressure conditions in cases of high eccentricities.展开更多
We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined wi...We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined with a finite element method and an operator splitting technique. As expected, a settling truncated cylinder turns its broadside perpendicular to the main stream direction and the center of mass moves to the central axis of the channel. In the case of two truncated cylinders, they first move around each other for a while and then stay together in a "T" shape. After the "T" shape has been formed for a long enough time, we found no vortex shedding behind the cylinders. When simulating the fluidization of 60 truncated cylinders, we captured the features of interactions among fluidized cylinders as observed in experiments.展开更多
This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characteri...This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.展开更多
A new online hybrid test system combined with substructuring techniques and incorporating finite element methods is developed.In the proposed system,numerical substructure analysis is conducted by ABAQUS/Explicit.An A...A new online hybrid test system combined with substructuring techniques and incorporating finite element methods is developed.In the proposed system,numerical substructure analysis is conducted by ABAQUS/Explicit.An ABAQUS user subroutine is used as the interface between the main control program and ABAQUS to impose the target displacements and determine the reaction forces.No iteration is needed in this system,making it suitable for physical testing.As the approach also avoids the need to modify source code,it will be appealing to a number of real engineering applications.The proposed system adopts a separated-model framework,operator-splitting integration scheme,and data exchange through a socket mechanism.The earthquake responses of a simple steel moment-resisting frame are simulated,and the results obtained from the new system are compared to those obtained from the conventional analysis.It is found that the results obtained from the new system are accurate,demonstrating the applicability and efficiency of the proposed approach.The optimal test parameters are also studied to gain the most accurate results in the minimum time.展开更多
A numerical method for coupled solution of the equations of groundwater flow and pollution transportation is presented on the basis of operator-splitting algorithm, and the application of Kalman filtering technique in...A numerical method for coupled solution of the equations of groundwater flow and pollution transportation is presented on the basis of operator-splitting algorithm, and the application of Kalman filtering technique into the study of groundwater pollution are explored also in the present paper. Computative examples indicate that the numerical method and application of Kalman theory can avoid the unhealthy tendencies in numerical modeling and hence attain the computative accuracy considerably.展开更多
基金the National Sciences Foundation of China and the Doctorial Program of Higher Edua-tion
文摘The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.
文摘This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.
文摘This paper presents an Operator -Splitting Method (OSM) for the solution of the universal Reynolds equation. Jakoobsson-Floberg-Olsson (JFO) pressure conditions were incorporated for the study of cavitation in a liquid-lubricated journal bearings. Shear flow component of the oil film was first solved by a modified upwind finite difference method. The solution of the pressure gradient flow component was completed by the Galerkin finite element method. Present OSM solutions for a slider bearing are in agreement with Elord's results. OSM was then applied to herringbone grooved journal bearing in this work. The film pressure, cavitation areas, load capacity and attitude angle were obtained with JFO pressure conditions. The calculated load capacities are in agreement with Hirs's experimental data. A comparison of the present results and those predicted by the Reynolds pressure conditions shows some differences. The numerical results indicate that the load capacity and the critical mass of journal (linear stability indicator) are higher, and the attitude angle is lower than those predicted by Reynolds pressure conditions in cases of high eccentricities.
文摘We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined with a finite element method and an operator splitting technique. As expected, a settling truncated cylinder turns its broadside perpendicular to the main stream direction and the center of mass moves to the central axis of the channel. In the case of two truncated cylinders, they first move around each other for a while and then stay together in a "T" shape. After the "T" shape has been formed for a long enough time, we found no vortex shedding behind the cylinders. When simulating the fluidization of 60 truncated cylinders, we captured the features of interactions among fluidized cylinders as observed in experiments.
文摘This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.
基金supported by the National Natural Science Foundation of China(Grant Nos.91315301 and 51422809)Tsinghua University Initiative Scientific Research Program(Grant No.2010Z01001)
文摘A new online hybrid test system combined with substructuring techniques and incorporating finite element methods is developed.In the proposed system,numerical substructure analysis is conducted by ABAQUS/Explicit.An ABAQUS user subroutine is used as the interface between the main control program and ABAQUS to impose the target displacements and determine the reaction forces.No iteration is needed in this system,making it suitable for physical testing.As the approach also avoids the need to modify source code,it will be appealing to a number of real engineering applications.The proposed system adopts a separated-model framework,operator-splitting integration scheme,and data exchange through a socket mechanism.The earthquake responses of a simple steel moment-resisting frame are simulated,and the results obtained from the new system are compared to those obtained from the conventional analysis.It is found that the results obtained from the new system are accurate,demonstrating the applicability and efficiency of the proposed approach.The optimal test parameters are also studied to gain the most accurate results in the minimum time.
文摘A numerical method for coupled solution of the equations of groundwater flow and pollution transportation is presented on the basis of operator-splitting algorithm, and the application of Kalman filtering technique into the study of groundwater pollution are explored also in the present paper. Computative examples indicate that the numerical method and application of Kalman theory can avoid the unhealthy tendencies in numerical modeling and hence attain the computative accuracy considerably.
