The complex geometric features of subsurface fractures at different scales makes mesh generation challenging and/or expensive.In this paper,we make use of neural style transfer(NST),a machine learning technique,to gen...The complex geometric features of subsurface fractures at different scales makes mesh generation challenging and/or expensive.In this paper,we make use of neural style transfer(NST),a machine learning technique,to generate mesh from rock fracture images.In this new approach,we use digital rock fractures at multiple scales that represent’content’and define uniformly shaped and sized triangles to represent’style’.The 19-layer convolutional neural network(CNN)learns the content from the rock image,including lower-level features(such as edges and corners)and higher-level features(such as rock,fractures,or other mineral fillings),and learns the style from the triangular grids.By optimizing the cost function to achieve approximation to represent both the content and the style,numerical meshes can be generated and optimized.We utilize the NST to generate meshes for rough fractures with asperities formed in rock,a network of fractures embedded in rock,and a sand aggregate with multiple grains.Based on the examples,we show that this new NST technique can make mesh generation and optimization much more efficient by achieving a good balance between the density of the mesh and the presentation of the geometric features.Finally,we discuss future applications of this approach and perspectives of applying machine learning to bridge the gaps between numerical modeling and experiments.展开更多
We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their dra...We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their drawbacks restrict their usages individually. Our algo- rithm combines the three steps together to make full use of their features. At first the Dirichlet energy is optimized for faster approximation with better topology. Then the area energy is used to come close to the constrained domain. Finally the DMC energy is engaged to achieve a better converging step. Results show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.展开更多
Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is ac...Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest.A sec- ond,less-popular method of spatial adaptivity is called'mesh motion'(r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales.This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function,the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone.Further,in an attempt to support the requirements of a very general class of climate simulation applications,the proposed method is de- signed to accommodate unstructured,polygonal mesh topologies in addition to the most popular mesh types.展开更多
In this paper,size and shape optimization problem of a machine gun system is addressed with an efficient hybrid method,in which a novel and flexible mesh morphing technique is employed to achieve fast parameterization...In this paper,size and shape optimization problem of a machine gun system is addressed with an efficient hybrid method,in which a novel and flexible mesh morphing technique is employed to achieve fast parameterization and modification of complexity structure without going back to CAD for reconstruction of geometric models or to finite element analysis（ FEA） for remodeling. Design of experiments（ DOE） and response surface method（ RSM） are applied to approximate the constitutive parameters of a machine gun system based on experimental tests. Further FEA,secondary development technique and genetic algorithm（ GA） are introduced to find all the optimal solutions in one go and the optimal design of the demonstrated machine gun system is obtained. Results of the rigid-flexible coupling dynamic analysis and exterior ballistics calculation validate the proposed methodology,which is relatively time-saving,reliable and has the potential to solve similar problems.展开更多
Two modeling methods of the root insert for wind turbine blade are presented,i.e.,the local mesh optimization method(LMOM)and the global modeling method(GMM).Based on the optimized mesh of the local model for the meta...Two modeling methods of the root insert for wind turbine blade are presented,i.e.,the local mesh optimization method(LMOM)and the global modeling method(GMM).Based on the optimized mesh of the local model for the metal contact interface,LMOM is proposed to analyze the load path and stress distribution characteristics,while GMM is used to calculate and analyze the stress distribution characteristics of the resin layer established between the bushing and composite layers of root insert.To validate the GMM,a tension test is carried out.The result successfully shows that the shear strain expresses a similar strain distribution tendency with the GMM′s results.展开更多
Image/video stitching is a technology for solving the field of view(FOV)limitation of images/videos.It stitches multiple overlapping images/videos to generate a wide-FOV image/video,and has been used in various fields...Image/video stitching is a technology for solving the field of view(FOV)limitation of images/videos.It stitches multiple overlapping images/videos to generate a wide-FOV image/video,and has been used in various fields such as sports broadcasting,video surveillance,street view,and entertainment.This survey reviews image/video stitching algorithms,with a particular focus on those developed in recent years.Image stitching first calculates the corresponding relationships between multiple overlapping images,deforms and aligns the matched images,and then blends the aligned images to generate a wide-FOV image.A seamless method is always adopted to eliminate such potential flaws as ghosting and blurring caused by parallax or objects moving across the overlapping regions.Video stitching is the further extension of image stitching.It usually stitches selected frames of original videos to generate a stitching template by performing image stitching algorithms,and the subsequent frames can then be stitched according to the template.Video stitching is more complicated with moving objects or violent camera movement,because these factors introduce jitter,shakiness,ghosting,and blurring.Foreground detection technique is usually combined into stitching to eliminate ghosting and blurring,while video stabilization algorithms are adopted to solve the jitter and shakiness.This paper further discusses panoramic stitching as a special-extension of image/video stitching.Panoramic stitching is currently the most widely used application in stitching.This survey reviews the latest image/video stitching methods,and introduces the fundamental principles/advantages/weaknesses of image/video stitching algorithms.Image/video stitching faces long-term challenges such as wide baseline,large parallax,and low-texture problem in the overlapping region.New technologies may present new opportunities to address these issues,such as deep learning-based semantic correspondence,and 3D image stitching.Finally,this survey discusses the challenges of image/video stitching and proposes potential solutions.展开更多
In this paper,we study the underlying properties of optimal Delaunay triangulations(ODT)and propose enhanced ODT methods combined with connectivity regularization.Based on optimizing node positions and Delaunay triang...In this paper,we study the underlying properties of optimal Delaunay triangulations(ODT)and propose enhanced ODT methods combined with connectivity regularization.Based on optimizing node positions and Delaunay triangulation iteratively,ODT methods are very effective in mesh improvement.This paper demonstrates that the energy function minimized by ODT is nonconvex and unsmooth,thus,ODT methods suffer the problem of falling into a local minimum inevitably.Unlike general ways that minimize the ODT energy function in terms of mathematics directly,we take an outflanking strategy combining ODT methods with connectivity regularization for this issue.Connectivity regularization reduces the number of irregular nodes by basic topological operations,which can be regarded as a perturbation to help ODT methods jump out of a poor local minimum.Although the enhanced ODT methods cannot guarantee to obtain a global minimum,it starts a new viewpoint of minimizing ODT energy which uses topological operations but mathematical methods.And in terms of practical effect,several experimental results illustrate the enhanced ODT methods are capable of improving the mesh furtherly compared to general ODT methods.展开更多
Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astroph...Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating.展开更多
ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuratio...ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.展开更多
An adaptive finite element procedure designed for specific computational goals is presented,using mesh refinement strategies based on optimal or nearly optimal a priori error estimates for the finite element method an...An adaptive finite element procedure designed for specific computational goals is presented,using mesh refinement strategies based on optimal or nearly optimal a priori error estimates for the finite element method and using estimators of the local regularity of the unknown exact solution derived from computed approximate solutions.The proposed procedure is analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that the method can generate the correct type of refinements and lead to the desired control under consideration.展开更多
The highlight line model is a powerful tool in assessing the quality of a surface. It increases the flexibility of an interactive design environment. In this paper, a method to generate a highlight line model on an ar...The highlight line model is a powerful tool in assessing the quality of a surface. It increases the flexibility of an interactive design environment. In this paper, a method to generate a highlight line model on an arbitrary triangular mesh is presented. Based on the highlight line model, a technique to remove local shape irregularities of a triangular mesh is then presented. The shape modification is done by solving a minimization problem and performing an iterative procedure. The new technique improves not only the shape quality of the mesh surface, but also the shape of the highlight line model. It provides an intuitive and yet suitable method for locally optimizing the shape of a triangular mesh.展开更多
3D modeling of tunnels using a nonlinear ground model is still a time-consuming task because it usually requires a large number of incremental phases with iterative processes,to ensure accuracy while minimizing comput...3D modeling of tunnels using a nonlinear ground model is still a time-consuming task because it usually requires a large number of incremental phases with iterative processes,to ensure accuracy while minimizing computational effort.Optimization of thefinite element mesh is of utmost importance.Despite the current tendency towards 3D modeling of tunnels,few publications are concerned with mesh optimization considering model size,grid refinement and order of elements.This paper improves the understanding of key issues that affect 3D modeling of tunnels.Our results shown that:(1)2nd order elements are more effcient when material nonlinearity is present and should be preferred;(2)the plastic zone size has a strong influence on the model dimensions and may require discretizations much larger than those currently accepted.The paper provides recommendations for mesh refinement and model dimensions(width and length)as a function of the plastic zone size,for accurate 3D models with reduced computational cost.展开更多
A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique(AFT)and conforming Delaunay triangulation.Given a triangulated surface mesh,AFT is firstly applied to ...A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique(AFT)and conforming Delaunay triangulation.Given a triangulated surface mesh,AFT is firstly applied to mesh several layers of elements adjacent to the boundary.The rest of the domain is then meshed by the conforming Delaunay triangulation.The non-conformal interface between two parts of meshes are adjusted.Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality.Robustness and quality of the proposed method is shown.Convergence proof of each stage as well as the whole algorithm is provided.Various numerical examples are included as well as the quality of the meshes.展开更多
In this paper we establish a high order finite volume method for the fourth order singular perturbation problems.In conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal co...In this paper we establish a high order finite volume method for the fourth order singular perturbation problems.In conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal convergence order.Numerical experiments are presented to verify our theoretical estimates.展开更多
The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the co...The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.展开更多
基金supported by Laboratory Directed Research and Development(LDRD)funding from Berkeley Laboratoryby the US Department of Energy(DOE),including the Office of Basic Energy Sciences,Chemical Sciences,Geosciences,and Biosciences Division and the Office of Nuclear Energy,Spent Fuel and Waste Disposition Campaign,both under Contract No.DEAC02-05CH11231 with Berkeley Laboratory。
文摘The complex geometric features of subsurface fractures at different scales makes mesh generation challenging and/or expensive.In this paper,we make use of neural style transfer(NST),a machine learning technique,to generate mesh from rock fracture images.In this new approach,we use digital rock fractures at multiple scales that represent’content’and define uniformly shaped and sized triangles to represent’style’.The 19-layer convolutional neural network(CNN)learns the content from the rock image,including lower-level features(such as edges and corners)and higher-level features(such as rock,fractures,or other mineral fillings),and learns the style from the triangular grids.By optimizing the cost function to achieve approximation to represent both the content and the style,numerical meshes can be generated and optimized.We utilize the NST to generate meshes for rough fractures with asperities formed in rock,a network of fractures embedded in rock,and a sand aggregate with multiple grains.Based on the examples,we show that this new NST technique can make mesh generation and optimization much more efficient by achieving a good balance between the density of the mesh and the presentation of the geometric features.Finally,we discuss future applications of this approach and perspectives of applying machine learning to bridge the gaps between numerical modeling and experiments.
基金Supported by the National Natural Science Foundation of China(11371320)Zhejiang Natural Science Foundation(LZ14A010002)+1 种基金Foundation of Science and Technology Department of Zhejiang Province(2013C31084)Scientific Research Fund of Zhejiang Provincial Education Department(Y201431077 and Y201329420)
文摘We analyze three commonly used energy functions in solving Plateau-Mesh Prob- lem, that is, Dirichlet, area, and the discrete mean curvature（DMC）. They all possess unique advantages compared to others, but their drawbacks restrict their usages individually. Our algo- rithm combines the three steps together to make full use of their features. At first the Dirichlet energy is optimized for faster approximation with better topology. Then the area energy is used to come close to the constrained domain. Finally the DMC energy is engaged to achieve a better converging step. Results show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.
文摘Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest.A sec- ond,less-popular method of spatial adaptivity is called'mesh motion'(r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales.This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function,the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone.Further,in an attempt to support the requirements of a very general class of climate simulation applications,the proposed method is de- signed to accommodate unstructured,polygonal mesh topologies in addition to the most popular mesh types.
基金Supported by the National Natural Science Foundation of China(51376090,51676099)
文摘In this paper,size and shape optimization problem of a machine gun system is addressed with an efficient hybrid method,in which a novel and flexible mesh morphing technique is employed to achieve fast parameterization and modification of complexity structure without going back to CAD for reconstruction of geometric models or to finite element analysis（ FEA） for remodeling. Design of experiments（ DOE） and response surface method（ RSM） are applied to approximate the constitutive parameters of a machine gun system based on experimental tests. Further FEA,secondary development technique and genetic algorithm（ GA） are introduced to find all the optimal solutions in one go and the optimal design of the demonstrated machine gun system is obtained. Results of the rigid-flexible coupling dynamic analysis and exterior ballistics calculation validate the proposed methodology,which is relatively time-saving,reliable and has the potential to solve similar problems.
基金supported jointly by the National Basic Research Program of China("973"Program)(No2014CB046200)the National Science Foundation of Jiangsu Province(No.BK2014059)+1 种基金the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe National Natural Science Foundation of China(No.11172135)
文摘Two modeling methods of the root insert for wind turbine blade are presented,i.e.,the local mesh optimization method(LMOM)and the global modeling method(GMM).Based on the optimized mesh of the local model for the metal contact interface,LMOM is proposed to analyze the load path and stress distribution characteristics,while GMM is used to calculate and analyze the stress distribution characteristics of the resin layer established between the bushing and composite layers of root insert.To validate the GMM,a tension test is carried out.The result successfully shows that the shear strain expresses a similar strain distribution tendency with the GMM′s results.
基金the National Natural Science Foundation of China(61872023).
文摘Image/video stitching is a technology for solving the field of view(FOV)limitation of images/videos.It stitches multiple overlapping images/videos to generate a wide-FOV image/video,and has been used in various fields such as sports broadcasting,video surveillance,street view,and entertainment.This survey reviews image/video stitching algorithms,with a particular focus on those developed in recent years.Image stitching first calculates the corresponding relationships between multiple overlapping images,deforms and aligns the matched images,and then blends the aligned images to generate a wide-FOV image.A seamless method is always adopted to eliminate such potential flaws as ghosting and blurring caused by parallax or objects moving across the overlapping regions.Video stitching is the further extension of image stitching.It usually stitches selected frames of original videos to generate a stitching template by performing image stitching algorithms,and the subsequent frames can then be stitched according to the template.Video stitching is more complicated with moving objects or violent camera movement,because these factors introduce jitter,shakiness,ghosting,and blurring.Foreground detection technique is usually combined into stitching to eliminate ghosting and blurring,while video stabilization algorithms are adopted to solve the jitter and shakiness.This paper further discusses panoramic stitching as a special-extension of image/video stitching.Panoramic stitching is currently the most widely used application in stitching.This survey reviews the latest image/video stitching methods,and introduces the fundamental principles/advantages/weaknesses of image/video stitching algorithms.Image/video stitching faces long-term challenges such as wide baseline,large parallax,and low-texture problem in the overlapping region.New technologies may present new opportunities to address these issues,such as deep learning-based semantic correspondence,and 3D image stitching.Finally,this survey discusses the challenges of image/video stitching and proposes potential solutions.
基金Supported by the National Natural Science Foundation of China(11802064)。
文摘In this paper,we study the underlying properties of optimal Delaunay triangulations(ODT)and propose enhanced ODT methods combined with connectivity regularization.Based on optimizing node positions and Delaunay triangulation iteratively,ODT methods are very effective in mesh improvement.This paper demonstrates that the energy function minimized by ODT is nonconvex and unsmooth,thus,ODT methods suffer the problem of falling into a local minimum inevitably.Unlike general ways that minimize the ODT energy function in terms of mathematics directly,we take an outflanking strategy combining ODT methods with connectivity regularization for this issue.Connectivity regularization reduces the number of irregular nodes by basic topological operations,which can be regarded as a perturbation to help ODT methods jump out of a poor local minimum.Although the enhanced ODT methods cannot guarantee to obtain a global minimum,it starts a new viewpoint of minimizing ODT energy which uses topological operations but mathematical methods.And in terms of practical effect,several experimental results illustrate the enhanced ODT methods are capable of improving the mesh furtherly compared to general ODT methods.
基金supported by the US Department of Energy Office of Science Climate Change Prediction Program through grant numbers DE-FG02-07ER64431 and DE-FG02-07ER64432the US National Science Foundation under grant numbers DMS-0609575 and DMS-0913491
文摘Centroidal Voronoi tessellations(CVTs) have become a useful tool in many applications ranging from geometric modeling,image and data analysis,and numerical partial differential equations,to problems in physics,astrophysics,chemistry,and biology. In this paper,we briefly review the CVT concept and a few of its generalizations and well-known properties.We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs.Whenever possible,we point out some outstanding issues that still need investigating.
基金supported by the National Natural Science Foundation of China(10472003)Beijing Natural Science(3002002)+1 种基金Beijing Educational Committee Foundations(KM200410005019)Suspensofled by American MSC Company.
文摘ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.
文摘An adaptive finite element procedure designed for specific computational goals is presented,using mesh refinement strategies based on optimal or nearly optimal a priori error estimates for the finite element method and using estimators of the local regularity of the unknown exact solution derived from computed approximate solutions.The proposed procedure is analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that the method can generate the correct type of refinements and lead to the desired control under consideration.
基金Supported by National Science Foundation of China (Grant Nos. 60533070, 60625202)National Basic Research Program of China (Grant No. 2004CB719400)+3 种基金National High-Tech Research & Development Program of China (Grant No. 2007AA040401)Fok Ying Tung Education Foundation (Grant No. 111070)National Science Foundation of USA (Grant Nos. DMI-0422126, DMS-0310645)Kentucky Science & Technology Corporation (Grant No. COMM-Fund-712)
文摘The highlight line model is a powerful tool in assessing the quality of a surface. It increases the flexibility of an interactive design environment. In this paper, a method to generate a highlight line model on an arbitrary triangular mesh is presented. Based on the highlight line model, a technique to remove local shape irregularities of a triangular mesh is then presented. The shape modification is done by solving a minimization problem and performing an iterative procedure. The new technique improves not only the shape quality of the mesh surface, but also the shape of the highlight line model. It provides an intuitive and yet suitable method for locally optimizing the shape of a triangular mesh.
基金supported by the research funding agency of Brazilian government CNPq("Conselho Nacional de Desenvolvimento Cientifico").
文摘3D modeling of tunnels using a nonlinear ground model is still a time-consuming task because it usually requires a large number of incremental phases with iterative processes,to ensure accuracy while minimizing computational effort.Optimization of thefinite element mesh is of utmost importance.Despite the current tendency towards 3D modeling of tunnels,few publications are concerned with mesh optimization considering model size,grid refinement and order of elements.This paper improves the understanding of key issues that affect 3D modeling of tunnels.Our results shown that:(1)2nd order elements are more effcient when material nonlinearity is present and should be preferred;(2)the plastic zone size has a strong influence on the model dimensions and may require discretizations much larger than those currently accepted.The paper provides recommendations for mesh refinement and model dimensions(width and length)as a function of the plastic zone size,for accurate 3D models with reduced computational cost.
基金Singapore MOE ARC 29/07 T207B2202,MOE RG 59/08 M52110092,NRF 2007IDM-IDM 002-010Natural Science Foundation of China 10971226 and 91130013,973 Program of China 2009CB723800the foundation of State Key Laboratory of Aerodynamics.
文摘A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique(AFT)and conforming Delaunay triangulation.Given a triangulated surface mesh,AFT is firstly applied to mesh several layers of elements adjacent to the boundary.The rest of the domain is then meshed by the conforming Delaunay triangulation.The non-conformal interface between two parts of meshes are adjusted.Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality.Robustness and quality of the proposed method is shown.Convergence proof of each stage as well as the whole algorithm is provided.Various numerical examples are included as well as the quality of the meshes.
基金the National Natural Science Foundation of China(Grant Nos.10771224,10601070)the Guangdong Provincial Natural Science Foundation of China(Grant No.05003308)+1 种基金MOE Project of Key Research Institute of Humanities and Social Sciences at UniversitiesChina-France-Russia Mathematics Collaboration(Grant No.34000-3275100)
文摘In this paper we establish a high order finite volume method for the fourth order singular perturbation problems.In conjunction with the optimal meshes,the numerical solutions resulting from the method have optimal convergence order.Numerical experiments are presented to verify our theoretical estimates.
基金supported by the National Natural Science Foundation of China(Grant No.11302110)the Public Project of Science and Technology Department of Zhejiang Province(Grant No.2015C31152)+1 种基金the Natural Science Foundation of Ningbo(Grant No.2014A610086)“Wang Weiming”Entrepreneurship Supporting Fund
文摘The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.
