In this Paper, a coupled natural boundary-finite element method is presented for solving three-dimensional Helmholtz equation in an unbounded domain.The existence and uniqueness of the solution for both continuous and...In this Paper, a coupled natural boundary-finite element method is presented for solving three-dimensional Helmholtz equation in an unbounded domain.The existence and uniqueness of the solution for both continuous and discrete problems are studied.Error estimated and some numerical results are given.展开更多
In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configura...In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.展开更多
为了研究RLC电路弹簧耦合系统的非线性振动,用统一的能量法考虑机电耦合系统的电场能、磁场能和机械能,应用拉格朗日-麦克斯韦方程建立起一个受到简谐激励的RLC电路弹簧耦合系统的数学模型,该机电耦合系统具有平方非线性。根据线性振动...为了研究RLC电路弹簧耦合系统的非线性振动,用统一的能量法考虑机电耦合系统的电场能、磁场能和机械能,应用拉格朗日-麦克斯韦方程建立起一个受到简谐激励的RLC电路弹簧耦合系统的数学模型,该机电耦合系统具有平方非线性。根据线性振动理论对系统运动微分方程组进行分析,得到了一个受简谐激励的M ath ieu方程,通过积分变换,得到了M ath ieu方程的级数形式解。分别用龙格库塔法和级数法计算了在无外激励的情况下,有阻尼和无阻尼时系统分别对应的时间响应,通过M atlab软件进行模拟分析,发现二者得到的响应曲线吻合,证明了级数法对分析类似系统是个很有效的手段。展开更多
Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance o...Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance of a highly loaded diffusion cascade with less suction slot. The effectiveness of the coupled method under different inlet boundary layers is also investigated.Results show that mid-span local boundary layer suction can effectively remove trailing edge separation, but deteriorate the flow fields near the endwall. The positive bowed cascade is beneficial for reducing open corner separation, but is detrimental to mid-span flow fields. The coupled method can further improve the performance and flow field of the cascade. The mid-span trailing edge separation and open corner separation are eliminated. Compared with linear cascade with suction, the coupled method reduces overall loss of the cascade by 31.4% at most. The mid-span loss of the cascade decreases as the suction coefficient increases, but increases as bow angle increases. The endwall loss increases as the suction coefficient increases. By contrast, the endwall loss decreases significantly as the bow angle increases. The endwall loss of coupled controlled cascade is higher than that of bowed cascade with the same bow angle because of the spanwise inverse ‘‘C＂ shaped static pressure distribution. Under different inlet boundary layer conditions, the coupled method can also improve the cascade effectively.展开更多
Based on the important boundary conditions of rolling simulation including friction, heat conduction and interactionsof the workpiece and rolls, the hot continuous rolling processes of large-diameter mandrel round bar...Based on the important boundary conditions of rolling simulation including friction, heat conduction and interactionsof the workpiece and rolls, the hot continuous rolling processes of large-diameter mandrel round bar (200 mm indiameter) in 6VH-stand hot tandem mill are successfully simulated by three-dimensional coupled thermomechanicalelastoplastic finite element method (FEM). The distributions of stress, strain, temperature and the rolling force andtorque for the two-pass and four-pass continuous rolling are calculated respectively. Thus, the two and four-passroll schedules are verified, respectively. The simulation results show that it is safe to produce 200 mm round barby the two-pass (oval pass and round pass) continuous rolling on the existing equipment compared to the four-passcontinuous rolling. There are concave surfaces and increased widths occurring at the end of rolled billet due touneven deformations between the outside and inside of the workpiece as well as the free spreading close to the rollgap of the final pass.展开更多
Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dime...Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.展开更多
In order to effectively cope with exponent increase of the complexity faced to the rock mechanics analysis problems and the large incompatibility existing between the information level required to model the rock mass ...In order to effectively cope with exponent increase of the complexity faced to the rock mechanics analysis problems and the large incompatibility existing between the information level required to model the rock mass and engineering and our obtainable information level at hand,the integrated approaches with intelligent characters are proposed. Many previous standard methods,such as precedent type analysis,rock classification,analytic method stress-based,basic numerical methods (BEM,FEM,DEM,hybrid),and their extended numerical methods (fully coupled) to be developed,can be selected respectively or integrated accordingly. It is alternative to develop basic/fully integrated system,and internet-based approaches. These novel methods can also be selected or integrated each other or with the standard methods to perform rock mechanics analysis. Some key techniques to develop these alternative methods are discussed. It may focus in future on developing fully integrated systems and internet-based approaches. Developing an environmental,virtual facility/space shall be firstly done for this collaborative research on internet.展开更多
This paper presents a developed new coupled method which combined our in-house CFD solver naoe-FOAM-SJTU and naoe-FOAM-os with a potential theory High Order Spectral method(HOS).A parametric study of nonlinear wave pr...This paper presents a developed new coupled method which combined our in-house CFD solver naoe-FOAM-SJTU and naoe-FOAM-os with a potential theory High Order Spectral method(HOS).A parametric study of nonlinear wave propagation in computational fluid dynamics(CFD)zone is considered.Mesh convergence,time step convergence,time discretization scheme and length of relaxation zone are all carried out.Those parametric studies verify the steady of this new combined method and give better choice for wave propagation.The dissipation in propagation of nonlinear regular wave can be lower than 3%in static mesh,and less than 2%in overset grid mesh.Meanwhile,a LNG FPSO is put into the viscous wave tank to study the suitable size of CFD zone.To achieve a better solution with least calculating resources and best numerical results,the length of CFD zone is discussed.These parametric studies can give reference upon employment of the potential-viscous coupled method and validation of the coupled method.展开更多
文摘In this Paper, a coupled natural boundary-finite element method is presented for solving three-dimensional Helmholtz equation in an unbounded domain.The existence and uniqueness of the solution for both continuous and discrete problems are studied.Error estimated and some numerical results are given.
文摘In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.
文摘为了研究RLC电路弹簧耦合系统的非线性振动,用统一的能量法考虑机电耦合系统的电场能、磁场能和机械能,应用拉格朗日-麦克斯韦方程建立起一个受到简谐激励的RLC电路弹簧耦合系统的数学模型,该机电耦合系统具有平方非线性。根据线性振动理论对系统运动微分方程组进行分析,得到了一个受简谐激励的M ath ieu方程,通过积分变换,得到了M ath ieu方程的级数形式解。分别用龙格库塔法和级数法计算了在无外激励的情况下,有阻尼和无阻尼时系统分别对应的时间响应,通过M atlab软件进行模拟分析,发现二者得到的响应曲线吻合,证明了级数法对分析类似系统是个很有效的手段。
基金supported by China Postdoctoral Science Foundationa key project of the National Natural Science Foundation of China (No. 51236006)
文摘Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance of a highly loaded diffusion cascade with less suction slot. The effectiveness of the coupled method under different inlet boundary layers is also investigated.Results show that mid-span local boundary layer suction can effectively remove trailing edge separation, but deteriorate the flow fields near the endwall. The positive bowed cascade is beneficial for reducing open corner separation, but is detrimental to mid-span flow fields. The coupled method can further improve the performance and flow field of the cascade. The mid-span trailing edge separation and open corner separation are eliminated. Compared with linear cascade with suction, the coupled method reduces overall loss of the cascade by 31.4% at most. The mid-span loss of the cascade decreases as the suction coefficient increases, but increases as bow angle increases. The endwall loss increases as the suction coefficient increases. By contrast, the endwall loss decreases significantly as the bow angle increases. The endwall loss of coupled controlled cascade is higher than that of bowed cascade with the same bow angle because of the spanwise inverse ‘‘C＂ shaped static pressure distribution. Under different inlet boundary layer conditions, the coupled method can also improve the cascade effectively.
文摘Based on the important boundary conditions of rolling simulation including friction, heat conduction and interactionsof the workpiece and rolls, the hot continuous rolling processes of large-diameter mandrel round bar (200 mm indiameter) in 6VH-stand hot tandem mill are successfully simulated by three-dimensional coupled thermomechanicalelastoplastic finite element method (FEM). The distributions of stress, strain, temperature and the rolling force andtorque for the two-pass and four-pass continuous rolling are calculated respectively. Thus, the two and four-passroll schedules are verified, respectively. The simulation results show that it is safe to produce 200 mm round barby the two-pass (oval pass and round pass) continuous rolling on the existing equipment compared to the four-passcontinuous rolling. There are concave surfaces and increased widths occurring at the end of rolled billet due touneven deformations between the outside and inside of the workpiece as well as the free spreading close to the rollgap of the final pass.
基金supported by National Natural Science Foundation of China(Grant No.11201239)the Singapore A*STAR SERC PSF(Grant No.1321202067)
文摘Due to the difficulty in obtaining the a priori estimate,it is very hard to establish the optimal point-wise error bound of a finite difference scheme for solving a nonlinear partial differential equation in high dimensions(2D or 3D).We here propose and analyze finite difference methods for solving the coupled GrossPitaevskii equations in two dimensions,which models the two-component Bose-Einstein condensates with an internal atomic Josephson junction.The methods which we considered include two conservative type schemes and two non-conservative type schemes.Discrete conservation laws and solvability of the schemes are analyzed.For the four proposed finite difference methods,we establish the optimal convergence rates for the error at the order of O(h^2+τ~2)in the l~∞-norm(i.e.,the point-wise error estimates)with the time stepτand the mesh size h.Besides the standard techniques of the energy method,the key techniques in the analysis is to use the cut-off function technique,transformation between the time and space direction and the method of order reduction.All the methods and results here are also valid and can be easily extended to the three-dimensional case.Finally,numerical results are reported to confirm our theoretical error estimates for the numerical methods.
基金Nature Science Foundation of China under Grant no.50179034.
文摘In order to effectively cope with exponent increase of the complexity faced to the rock mechanics analysis problems and the large incompatibility existing between the information level required to model the rock mass and engineering and our obtainable information level at hand,the integrated approaches with intelligent characters are proposed. Many previous standard methods,such as precedent type analysis,rock classification,analytic method stress-based,basic numerical methods (BEM,FEM,DEM,hybrid),and their extended numerical methods (fully coupled) to be developed,can be selected respectively or integrated accordingly. It is alternative to develop basic/fully integrated system,and internet-based approaches. These novel methods can also be selected or integrated each other or with the standard methods to perform rock mechanics analysis. Some key techniques to develop these alternative methods are discussed. It may focus in future on developing fully integrated systems and internet-based approaches. Developing an environmental,virtual facility/space shall be firstly done for this collaborative research on internet.
基金supported by the National Natural Science Foundation of China(Grant Nos.51879159,51809169 and 51909160)the National Key Research and Development Program of China(Grant Nos.2019YFB1704200,2019YFC0312400)+1 种基金supported by the Chang Jiang Scholars Program(Grant No.T2014099)the Innovative Special Project of Numerical Tank of Ministry of Industry and Information Technology of China(Grant No.2016-23/09).
文摘This paper presents a developed new coupled method which combined our in-house CFD solver naoe-FOAM-SJTU and naoe-FOAM-os with a potential theory High Order Spectral method(HOS).A parametric study of nonlinear wave propagation in computational fluid dynamics(CFD)zone is considered.Mesh convergence,time step convergence,time discretization scheme and length of relaxation zone are all carried out.Those parametric studies verify the steady of this new combined method and give better choice for wave propagation.The dissipation in propagation of nonlinear regular wave can be lower than 3%in static mesh,and less than 2%in overset grid mesh.Meanwhile,a LNG FPSO is put into the viscous wave tank to study the suitable size of CFD zone.To achieve a better solution with least calculating resources and best numerical results,the length of CFD zone is discussed.These parametric studies can give reference upon employment of the potential-viscous coupled method and validation of the coupled method.
