Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,acco...Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,according to the recent research,applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law(GCL)is not satisfied,and this may cause numerical instability.To cope with this problem,a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme(HDCS)has been formulated.The formulation of the HDCS contains two steps.First,a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL,and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables.The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry,while the DCS may suffer numerical instabilities.Moreover,high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.展开更多
The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algeb...The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.展开更多
The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element ...The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.展开更多
Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boun...Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary(IB)method developed in our previous work.For the moving structure modeled using the sharp interface IB method,a recursive box method is developed for efficiently classifying the background grid nodes.For the particles modeled using the diffuse interface IB method,a‘master-slave’approach is adopted.For the particle-particle interaction(PPI)and particle-structure interaction(PSI),a fast algorithm for classifying the active and inactive Lagrangian points,which discretize the particle surface,is developed for the‘dry’contact approach.The results show that the proposed recursive box method can reduce the classifying time from 52seconds to 0.3 seconds.Acceptable parallel efficiency is obtained for cases with different particle concentrations.Furthermore,the lubrication model is utilized when a particle approaches a wall,enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem.At last,the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls.展开更多
Springback of a SUS321 complex geometry part formed by the multi-stage rigid-flexible compound process was studied through numerical simulations and laboratory experiments in this work.The sensitivity analysis was pro...Springback of a SUS321 complex geometry part formed by the multi-stage rigid-flexible compound process was studied through numerical simulations and laboratory experiments in this work.The sensitivity analysis was provided to have an insight in the effect of the evaluated process parameters.Furthermore,in order to minimize the springback problem,an accurate springback simulation model of the part was established and validated.The effects of the element size and timesteps on springback model were further investigated.Results indicate that the custom mesh size is beneficial for the springback simulation,and the four timesteps are found suited for the springback analysis for the complex geometry part.Finally,a strategy for reducing the springback by changing the geometry of the blank is proposed.The optimal blank geometry is obtained and used for manufacturing the part.展开更多
Crystal structure of the title compound, (NO 3) 2·4H 2O (Im=imidazole), was determined by X-ray crystallographic analysis. The crystal structure consists of discrete Ni^(Im) 2+ 6 cation, NO - 3 anion and...Crystal structure of the title compound, (NO 3) 2·4H 2O (Im=imidazole), was determined by X-ray crystallographic analysis. The crystal structure consists of discrete Ni^(Im) 2+ 6 cation, NO - 3 anion and four uncoordinated water molecules. It crystallizes in the hexagonal system, space group P63, with lattice parameters a=b= 0.9003(2) nm, c= 2.1034(4) nm, and Z=2. The Ni(II) ion is centro- symmetric octahedron geometry with the NiN 6 core. Six imidazole molecules are coordinated to each nickel(II) atom through its tertiary nitrogen atom. The short and long bond distances of Ni-N are 0.2059(6) and 0.2204(7) nm, respectively. In the solid state, 2+, H 2O moieties and nitrate anions form the three dimensional hydrogen bonds network which stabitizes the crystal structure.展开更多
基金supported by the National Basic Research Program of China(Grant no.2009CB723800)National Natural Science Foundation of China(Grand Nos.11072259 and 11202226)the Foundation of State Key Laboratory of Aerodynamics(Grand Nos.JBKY11030902 and JBKY11010100)
文摘Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study.High resolution has been achieved by Dissipative Compact Schemes(DCS),however,according to the recent research,applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law(GCL)is not satisfied,and this may cause numerical instability.To cope with this problem,a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme(HDCS)has been formulated.The formulation of the HDCS contains two steps.First,a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL,and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables.The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry,while the DCS may suffer numerical instabilities.Moreover,high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.
基金supported by a grant from the National Science Foundation.
文摘The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed.
基金Project supported by the National Natural Science Foundation of China (Nos. 12102043, 12072375U2241240)the Natural Science Foundation of Hunan Province of China (Nos. 2023JJ40698 and 2021JJ40710)。
文摘The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.
基金Project supported by the National Natural Science Foundation of China(Nos.12202456 and12172360)the Basic Science Center Program for“Multiscale Problems in Nonlinear Mechanics”of the National Natural Science Foundation of China(No.11988102)the China Postdoctoral Science Foundation(No.2021M693241)。
文摘Fluid-structure-particle interactions in three spatial dimensions happen in many environmental and engineering flows.This paper presents the parallel algorithms for the hybrid diffuse and sharp interface immersed boundary(IB)method developed in our previous work.For the moving structure modeled using the sharp interface IB method,a recursive box method is developed for efficiently classifying the background grid nodes.For the particles modeled using the diffuse interface IB method,a‘master-slave’approach is adopted.For the particle-particle interaction(PPI)and particle-structure interaction(PSI),a fast algorithm for classifying the active and inactive Lagrangian points,which discretize the particle surface,is developed for the‘dry’contact approach.The results show that the proposed recursive box method can reduce the classifying time from 52seconds to 0.3 seconds.Acceptable parallel efficiency is obtained for cases with different particle concentrations.Furthermore,the lubrication model is utilized when a particle approaches a wall,enabling an accurate simulation of the rebounding phenomena in the benchmark particle-wall collision problem.At last,the capability of the proposed computational framework is demonstrated by simulating particle-laden turbulent channel flows with rough walls.
基金Project(2014ZX04002041)supported by the National Science and Technology Major Project,ChinaProject(51175024)supported by the National Natural Science Foundation of China
文摘Springback of a SUS321 complex geometry part formed by the multi-stage rigid-flexible compound process was studied through numerical simulations and laboratory experiments in this work.The sensitivity analysis was provided to have an insight in the effect of the evaluated process parameters.Furthermore,in order to minimize the springback problem,an accurate springback simulation model of the part was established and validated.The effects of the element size and timesteps on springback model were further investigated.Results indicate that the custom mesh size is beneficial for the springback simulation,and the four timesteps are found suited for the springback analysis for the complex geometry part.Finally,a strategy for reducing the springback by changing the geometry of the blank is proposed.The optimal blank geometry is obtained and used for manufacturing the part.
基金SupportedbyEducationalAdministrationKeyProjectofShandongProvince (No .J0 1C0 5 )andtheOutstandingAdult YoungScientificResearchEncouragingFoundationofShandongProvince (No .O1BS18)
文摘Crystal structure of the title compound, (NO 3) 2·4H 2O (Im=imidazole), was determined by X-ray crystallographic analysis. The crystal structure consists of discrete Ni^(Im) 2+ 6 cation, NO - 3 anion and four uncoordinated water molecules. It crystallizes in the hexagonal system, space group P63, with lattice parameters a=b= 0.9003(2) nm, c= 2.1034(4) nm, and Z=2. The Ni(II) ion is centro- symmetric octahedron geometry with the NiN 6 core. Six imidazole molecules are coordinated to each nickel(II) atom through its tertiary nitrogen atom. The short and long bond distances of Ni-N are 0.2059(6) and 0.2204(7) nm, respectively. In the solid state, 2+, H 2O moieties and nitrate anions form the three dimensional hydrogen bonds network which stabitizes the crystal structure.
