Multi-scale problems in Computational Fluid Dynamics(CFD)often require numerous simulations across various design parameters.Using a fixed mesh for all cases may fail to capture critical physical features.Moving mesh ...Multi-scale problems in Computational Fluid Dynamics(CFD)often require numerous simulations across various design parameters.Using a fixed mesh for all cases may fail to capture critical physical features.Moving mesh adaptation provides an optimal resource allocation to obtain high-resolution flow-fields on low-resolution meshes.However,most existing methods require manual experience and the flow posteriori information poses great challenges to practical applications.In addition,generating adaptive meshes directly from design parameters is difficult due to highly nonlinear relationships.The diffusion model is currently the most popular model in generative tasks that integrates the diffusion principle into deep learning to capture the complex nonlinear correlations.A dual diffusion framework,Para2Mesh,is proposed to predict the adaptive meshes from design parameters by exploiting the robust data distribution learning ability of the diffusion model.Through iterative denoising,the proposed dual networks accurately reconstruct the flow-field to provide flow features as supervised information,and then achieve rapid and reliable mesh movement.Experiments in CFD scenarios demonstrate that Para2Mesh predicts similar meshes directly from design parameters with much higher efficiency than traditional method.It could become a real-time adaptation tool to assist engineering design and optimization,providing a promising solution for high-resolution flow-field analysis.展开更多
Computational mesh is an important ingredient that affects the accuracy and efficiency of CFD numerical simulation.In light of the introduced large amount of computational costs for many adaptive mesh methods,moving m...Computational mesh is an important ingredient that affects the accuracy and efficiency of CFD numerical simulation.In light of the introduced large amount of computational costs for many adaptive mesh methods,moving mesh methods keep the number of nodes and topology of a mesh unchanged and do not increase CFD computational expense.As the state-of-the-art moving mesh method,the variational mesh adaptation approach has been introduced to CFD calculation.However,quickly estimating the flow field on the updated meshes during the iterative algorithm is challenging.A mesh optimization method,which embeds a machine learning regression model into the variational mesh adaptation,is proposed.The regression model captures the mapping between the initial mesh nodes and the flow field,so that the variational method could move mesh nodes iteratively by solving the mesh functional which is built from the estimated flow field on the updated mesh via the regression model.After the optimization,the density of the nodes in the high gradient area increases while the density in the low gradient area decreases.Benchmark examples are first used to verify the feasibility and effectiveness of the proposed method.And then we use the steady subsonic and transonic flows over cylinder and NACA0012 airfoil on unstructured triangular meshes to test our method.Results show that the proposed method significantly improves the accuracy of the local flow features on the adaptive meshes.Our work indicates that the proposed mesh optimization approach is promising for improving the accuracy and efficiency of CFD computation.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
Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolat...Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.展开更多
Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation o...Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation of new holes.However,most pertinent investigations in the field rely predominantly on fixed background mesh,which is never remeshed.Consequently,the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties.This paper introduces a novel approach to topology op-timization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter.Primarily,combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface.This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process,but also improves the accuracy of calculation.Additionally,the incorporation of a Helmholtz-type partial differential equation filter,relying solely on mesh information essential for finite element discretization,serves to regulate the topological complexity and the minimum feature size of the optimized structure.Leveraging these advantages,the topology optimization program demonstrates its versa-tility by successfully addressing various design problems,encompassing the minimum mean compliance problem and minimum energy dissipation problem.Ultimately,the result of numerical example indicates that the optimized structure exhibits a dis-tinct and smooth boundary,affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.展开更多
Mesh adaptation is studied from the mesh control point of view.Two principles,equidistribution and alignment,are obtained and found to be necessary and sufficient for a complete control of the size,shape,and orientati...Mesh adaptation is studied from the mesh control point of view.Two principles,equidistribution and alignment,are obtained and found to be necessary and sufficient for a complete control of the size,shape,and orientation of mesh elements.A key component in these principles is the monitor function,a symmetric and positive definite matrix used for specifying the mesh information.A monitor function is defined based on interpolation error in a way with which an error bound is minimized on a mesh satisfying the equidistribution and alignment conditions.Algorithms for generating meshes satisfying the conditions are developed and two-dimensional numerical results are presented.展开更多
In present paper,mesh adaptation is applied for curing the pathological behaviors of the enhanced time-accurate upwind scheme(Loh&Jorgenson,AIAAJ 2016).In the original ETAU(enhanced time-accurate upwind)scheme,a m...In present paper,mesh adaptation is applied for curing the pathological behaviors of the enhanced time-accurate upwind scheme(Loh&Jorgenson,AIAAJ 2016).In the original ETAU(enhanced time-accurate upwind)scheme,a multidimensional dissipation model is required to cure the pathological behaviors.The multi-dimensional dissipation model will increase the global dissipation level reducing numerical resolution.In present work,the metric-based mesh adaptation strategy provides an alternative way to cure the pathological behaviors of the shock capturing.The Hessian matrix of flow variables is applied to construct the metric,which represents the curvature of the physical solution.The adapting operation can well refine the anisotropic meshes at the location with large gradients.The numerical results show that the adaptation of mesh provides a possible way to cure the pathological behaviors of upwind schemes.展开更多
In this work,vortex convection is simulated using a dynamic mesh adaptation procedure.In each adaptation period,the mesh is refined in the regions where the phenomena evolve and is coarsened in the regions where the p...In this work,vortex convection is simulated using a dynamic mesh adaptation procedure.In each adaptation period,the mesh is refined in the regions where the phenomena evolve and is coarsened in the regions where the phenomena deviate since the last adaptation.A simple indicator of mesh adaptation that accounts for the solution progression is defined.The generation of dynamic adaptive meshes is based on multilevel refinement/coarsening.The efficiency and accuracy of the present procedure are validated by simulating vortex convection in a uniform flow.Two unsteady compressible turbulent flows involving blade-vortex interactions are investigated to demonstrate further the applicability of the procedure.Computed results agree well with the published experimental data or numerical results.展开更多
Semi-crystalline polymer laser powder bed fusion(L-PBF)has recently attracted increasing interest due to its potential for fabricating complex geometry.However,a more comprehensive understanding of the underlying phys...Semi-crystalline polymer laser powder bed fusion(L-PBF)has recently attracted increasing interest due to its potential for fabricating complex geometry.However,a more comprehensive understanding of the underlying physics during L-PBF is required to better control the properties of the final part.This work proposed a multi-layer numerical model to study the temperature and phase evolution during the polyamide-12(PA12)L-PBF process.The Descend and Parallel Chord methods were introduced to improve the convergence of the non-linear thermal solver.The level-set-based mesh adaptation strategy,governed by multi-physical fields,was applied to alleviate the calculation and accurately track the phase evolution.The processing simulation on the dog-bone model revealed that preheating temperature significantly influences the crystallization behavior.Finally,the multi-layer simulation demonstrated that such a developed numerical model can be used to study the phase transformation during powder layer updating and the cyclic laser sintering phenomena.Moreover,the numerical study suggested that crystallization occurs slowly during the L-PBF process.展开更多
The wing of a butterfly consists of partially overlapping forewing and hindwing,and forewing sweeping can dynamically change the shape of the whole wing.In this work,the effect of forewing sweeping on aerodynamic perf...The wing of a butterfly consists of partially overlapping forewing and hindwing,and forewing sweeping can dynamically change the shape of the whole wing.In this work,the effect of forewing sweeping on aerodynamic performance of a butterfly like model is studied using a solver based on immersed boundary method and adaptive mesh.For aerodynamic performance,adding a"forward-backward-forward"sweeping motion to the forewing makes it more suitable for fast cruising flight,and compared to the situation without forewing sweeping,the drag is reduced by 46%and the lift to drag ratio is increased by 45%.On the contrary,adding a"backward-for ward-backward"sweeping motion to the forewing increases lift and makes it more suitable for climb flight.For downstroke and middle to late upstroke,the forewing sweeping affects the Leading-Edge Vortex(LEV)through two factors:sweeping velocity and forward sweeping angle,and their effects are coupled.A large forward sweeping velocity can enhance the strength of LEV,while a large forward sweeping angle can weaken it.For early upstroke,the forewing sweeping can affect the wake capture mechanism,sweeping backward can enhance it while sweeping forward can weaken it.The findings in this work provide insight into the design of butterfly like Micro AirVehicles(MAVs).展开更多
Simulation of the microstructure evolution during solidifi cation is greatly benefi cial to the control of solidifi cation microstructures. A phase-fi eld method based on the full threaded tree(FTT) for the simulation...Simulation of the microstructure evolution during solidifi cation is greatly benefi cial to the control of solidifi cation microstructures. A phase-fi eld method based on the full threaded tree(FTT) for the simulation of casting solidifi cation microstructure was proposed in this paper, and the structure of the full threaded tree and the mesh refi nement method was discussed. During dendritic growth in solidifi cation, the mesh for simulation is adaptively refi ned at the liquid-solid interface, and coarsened in other areas. The numerical results of a threedimension dendrite growth indicate that the phase-fi eld method based on FTT is suitable for microstructure simulation. Most importantly, the FTT method can increase the spatial and temporal resolutions beyond the limits imposed by the available hardware compared with the conventional uniform mesh. At the simulation time of 0.03 s in this study, the computer memory used for computation is no more than 10 MB with the FTT method, while it is about 50 MB with the uniform mesh method. In addition, the proposed FTT method is more effi cient in computation time when compared with the uniform mesh method. It would take about 20 h for the uniform mesh method, while only 2 h for the FTT method for computation when the solidifi cation time is 0.17 s in this study.展开更多
In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstructio...In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.展开更多
A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on α priori （sequentially） adapted meshes and study its convergence...A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on α priori （sequentially） adapted meshes and study its convergence. The scheme on α priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find α priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in χ, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for improving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical solution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N^-1 = o （ε^v）, where N denotes the number of nodes in the spatial mesh, and the value v = v（K） can be chosen arbitrarily small for suitable K.展开更多
A combined characteristic-based split algorithm and all adaptive meshing technique for analyzing two-dimensional viscous incompressible flow are presented. Tile method uses the three-node triangular element with equal...A combined characteristic-based split algorithm and all adaptive meshing technique for analyzing two-dimensional viscous incompressible flow are presented. Tile method uses the three-node triangular element with equal-order interpolation functions for all variables of tile velocity components and pressure. The main advantage of the combined nlethod is that it inlproves the sohltion accuracy by coupling an error estinla- tion procedure to an adaptive meshing technique that generates small elements in regions with a large change ill sohmtion gradients, mid at the same time, larger elements in the other regions. The performance of the combined procedure is evaluated by analyzing one test case of the flow past a cylinder, for their transient and steady-state flow behaviors.展开更多
High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic （CAA） problems with an aim at improving computational efficiency. A number of numerical i...High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic （CAA） problems with an aim at improving computational efficiency. A number of numerical issues associated with high-order schemes on an adaptively refined mesh, such as stability and accuracy are addressed. Several CAA benchmark problems are used to demonstrate the feasibility and efficiency of the approach.展开更多
The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a cons...The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a conservative spatial interpolation, the time integration methodology with the adapitve time increment and an adaptive computational region method. The advantage of AMR technique is exhibited by numerical examples, including the 1-D C-J detonation and the 2-D implosion ignited from a single point. Results show that AMR can promote the computational efficiency, keeping the accuracy in interesting regions.展开更多
The adaptive mesh mesh technique is developed and applied in three dimensional numerical simulation of welding process on the base of the commercial software. Special user subroutine is worked out to accom- plish t...The adaptive mesh mesh technique is developed and applied in three dimensional numerical simulation of welding process on the base of the commercial software. Special user subroutine is worked out to accom- plish this function.This technique can make the dense mesh moving simultaneously with the heat source while the other area of the structure with much coarser mesh, greatly reducing the number of nodes and elements in the analysis.Temperature field,displacement and stress distributions during welding pro- cess me analyzed by FEM method with adaptive mesh and the analysis is also conducted with normal FEM method. The temperature field,displacement and stress distributions obtained with both methods are shown in contrast. The results show that the temperature fields and the displacement distributions of simulation on adaptive mesh correspond wery well with that of without adaptive mesh. Though the stress distributions have some difference,but the trends of the stress distribution are corresponding.The com- parison of the computing time of the two meshes indicates that the adaptive that the adaptive mesh can greatly reduce the calculation time when used for welding process.展开更多
In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical featu...In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.展开更多
The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stok...The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations.The octree structure mesh is employed to solve the flow velocities and the pressure.The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity.The numerical results well predict the shape evolution of the droplet.展开更多
The technique of adaptive tree mesh is an effective way to reduce computational cost through automatic adjustment of cell size according to necessity. In the present study, the 2D numerical N-S solver based on the ada...The technique of adaptive tree mesh is an effective way to reduce computational cost through automatic adjustment of cell size according to necessity. In the present study, the 2D numerical N-S solver based on the adaptive quadtree mesh system was extended to a 3D one, in which a spatially adaptive oetree mesh system and multiple particle level set method were adopted for the convenience to deal with the air-water-structure multiple-medium coexisting domain. The stretching process of a dumbbell was simulated and the results indicate that the meshes are well adaptable to the free surface. The collapsing process of water column impinging a circle cylinder was simulated and from the results, it can be seen that the processes of fluid splitting and merging are properly simulated. The interaction of second-order Stokes waves with a square cylinder was simulated and the obtained drag force is consistent with the result by the Morison＇s wave force formula with the coefficient values of the stable drag component and the inertial force component bein~ set as 2.54.展开更多
基金co-supported by the Aeronautical Science Foundation of China(Nos.2018ZA52002 and 2019ZA052011)。
文摘Multi-scale problems in Computational Fluid Dynamics(CFD)often require numerous simulations across various design parameters.Using a fixed mesh for all cases may fail to capture critical physical features.Moving mesh adaptation provides an optimal resource allocation to obtain high-resolution flow-fields on low-resolution meshes.However,most existing methods require manual experience and the flow posteriori information poses great challenges to practical applications.In addition,generating adaptive meshes directly from design parameters is difficult due to highly nonlinear relationships.The diffusion model is currently the most popular model in generative tasks that integrates the diffusion principle into deep learning to capture the complex nonlinear correlations.A dual diffusion framework,Para2Mesh,is proposed to predict the adaptive meshes from design parameters by exploiting the robust data distribution learning ability of the diffusion model.Through iterative denoising,the proposed dual networks accurately reconstruct the flow-field to provide flow features as supervised information,and then achieve rapid and reliable mesh movement.Experiments in CFD scenarios demonstrate that Para2Mesh predicts similar meshes directly from design parameters with much higher efficiency than traditional method.It could become a real-time adaptation tool to assist engineering design and optimization,providing a promising solution for high-resolution flow-field analysis.
基金co-supported by the Key Laboratory of Aerodynamic Noise Control,China(No.ANCL20190103)the State Key Laboratory of Aerodynamics,China(No.SKLA20180102)the Aeronautical Science Foundation of China(Nos.2018ZA52002 and 2019ZA052011)。
文摘Computational mesh is an important ingredient that affects the accuracy and efficiency of CFD numerical simulation.In light of the introduced large amount of computational costs for many adaptive mesh methods,moving mesh methods keep the number of nodes and topology of a mesh unchanged and do not increase CFD computational expense.As the state-of-the-art moving mesh method,the variational mesh adaptation approach has been introduced to CFD calculation.However,quickly estimating the flow field on the updated meshes during the iterative algorithm is challenging.A mesh optimization method,which embeds a machine learning regression model into the variational mesh adaptation,is proposed.The regression model captures the mapping between the initial mesh nodes and the flow field,so that the variational method could move mesh nodes iteratively by solving the mesh functional which is built from the estimated flow field on the updated mesh via the regression model.After the optimization,the density of the nodes in the high gradient area increases while the density in the low gradient area decreases.Benchmark examples are first used to verify the feasibility and effectiveness of the proposed method.And then we use the steady subsonic and transonic flows over cylinder and NACA0012 airfoil on unstructured triangular meshes to test our method.Results show that the proposed method significantly improves the accuracy of the local flow features on the adaptive meshes.Our work indicates that the proposed mesh optimization approach is promising for improving the accuracy and efficiency of CFD computation.
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.
文摘Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.
基金supported by the National Natural Science Foundation of China(Grant Nos.12372200 and 12072242).
文摘Parameterized level-set method(PLSM)has been proposed and developed for many years,and is renowned for its efficacy in ad-dressing topology optimization challenges associated with intricate boundaries and nucleation of new holes.However,most pertinent investigations in the field rely predominantly on fixed background mesh,which is never remeshed.Consequently,the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties.This paper introduces a novel approach to topology op-timization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter.Primarily,combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface.This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process,but also improves the accuracy of calculation.Additionally,the incorporation of a Helmholtz-type partial differential equation filter,relying solely on mesh information essential for finite element discretization,serves to regulate the topological complexity and the minimum feature size of the optimized structure.Leveraging these advantages,the topology optimization program demonstrates its versa-tility by successfully addressing various design problems,encompassing the minimum mean compliance problem and minimum energy dissipation problem.Ultimately,the result of numerical example indicates that the optimized structure exhibits a dis-tinct and smooth boundary,affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.
基金supported in part by the NSF under grant DMS-0410545.
文摘Mesh adaptation is studied from the mesh control point of view.Two principles,equidistribution and alignment,are obtained and found to be necessary and sufficient for a complete control of the size,shape,and orientation of mesh elements.A key component in these principles is the monitor function,a symmetric and positive definite matrix used for specifying the mesh information.A monitor function is defined based on interpolation error in a way with which an error bound is minimized on a mesh satisfying the equidistribution and alignment conditions.Algorithms for generating meshes satisfying the conditions are developed and two-dimensional numerical results are presented.
基金the financial support received from the National Natural Science Foundation of China,under Grant No.91841302 and No.51976184the Basic Science Center Program for Multiphase Evolution in Hypergravity of the National Natural Science Foundation of China(No.51988101)the Fundamental Research Funds for the Central Universities(No.2019QNA4034).
文摘In present paper,mesh adaptation is applied for curing the pathological behaviors of the enhanced time-accurate upwind scheme(Loh&Jorgenson,AIAAJ 2016).In the original ETAU(enhanced time-accurate upwind)scheme,a multidimensional dissipation model is required to cure the pathological behaviors.The multi-dimensional dissipation model will increase the global dissipation level reducing numerical resolution.In present work,the metric-based mesh adaptation strategy provides an alternative way to cure the pathological behaviors of the shock capturing.The Hessian matrix of flow variables is applied to construct the metric,which represents the curvature of the physical solution.The adapting operation can well refine the anisotropic meshes at the location with large gradients.The numerical results show that the adaptation of mesh provides a possible way to cure the pathological behaviors of upwind schemes.
基金National Science Foundation of China under Grant 11072113.
文摘In this work,vortex convection is simulated using a dynamic mesh adaptation procedure.In each adaptation period,the mesh is refined in the regions where the phenomena evolve and is coarsened in the regions where the phenomena deviate since the last adaptation.A simple indicator of mesh adaptation that accounts for the solution progression is defined.The generation of dynamic adaptive meshes is based on multilevel refinement/coarsening.The efficiency and accuracy of the present procedure are validated by simulating vortex convection in a uniform flow.Two unsteady compressible turbulent flows involving blade-vortex interactions are investigated to demonstrate further the applicability of the procedure.Computed results agree well with the published experimental data or numerical results.
文摘Semi-crystalline polymer laser powder bed fusion(L-PBF)has recently attracted increasing interest due to its potential for fabricating complex geometry.However,a more comprehensive understanding of the underlying physics during L-PBF is required to better control the properties of the final part.This work proposed a multi-layer numerical model to study the temperature and phase evolution during the polyamide-12(PA12)L-PBF process.The Descend and Parallel Chord methods were introduced to improve the convergence of the non-linear thermal solver.The level-set-based mesh adaptation strategy,governed by multi-physical fields,was applied to alleviate the calculation and accurately track the phase evolution.The processing simulation on the dog-bone model revealed that preheating temperature significantly influences the crystallization behavior.Finally,the multi-layer simulation demonstrated that such a developed numerical model can be used to study the phase transformation during powder layer updating and the cyclic laser sintering phenomena.Moreover,the numerical study suggested that crystallization occurs slowly during the L-PBF process.
基金supported by the National Natural Science Foundation of China(No.52175277)The computations were conducted in Computing Center in Xi'an.The authors thankfully acknowledge these institutions.
文摘The wing of a butterfly consists of partially overlapping forewing and hindwing,and forewing sweeping can dynamically change the shape of the whole wing.In this work,the effect of forewing sweeping on aerodynamic performance of a butterfly like model is studied using a solver based on immersed boundary method and adaptive mesh.For aerodynamic performance,adding a"forward-backward-forward"sweeping motion to the forewing makes it more suitable for fast cruising flight,and compared to the situation without forewing sweeping,the drag is reduced by 46%and the lift to drag ratio is increased by 45%.On the contrary,adding a"backward-for ward-backward"sweeping motion to the forewing increases lift and makes it more suitable for climb flight.For downstroke and middle to late upstroke,the forewing sweeping affects the Leading-Edge Vortex(LEV)through two factors:sweeping velocity and forward sweeping angle,and their effects are coupled.A large forward sweeping velocity can enhance the strength of LEV,while a large forward sweeping angle can weaken it.For early upstroke,the forewing sweeping can affect the wake capture mechanism,sweeping backward can enhance it while sweeping forward can weaken it.The findings in this work provide insight into the design of butterfly like Micro AirVehicles(MAVs).
基金financially supported by Program for New Century Excellent Talents in University(No.NCET-090396)the Foundation for Innovative Research Groups of the Natural Science Foundation of Hubei Province,China(2010CDA067)State Major Science and Technology Special Project Foundation for High-end Numerical Machine and Basic Manufacturing Equipment(2011ZX04014-052,2012ZX04012-011)
文摘Simulation of the microstructure evolution during solidifi cation is greatly benefi cial to the control of solidifi cation microstructures. A phase-fi eld method based on the full threaded tree(FTT) for the simulation of casting solidifi cation microstructure was proposed in this paper, and the structure of the full threaded tree and the mesh refi nement method was discussed. During dendritic growth in solidifi cation, the mesh for simulation is adaptively refi ned at the liquid-solid interface, and coarsened in other areas. The numerical results of a threedimension dendrite growth indicate that the phase-fi eld method based on FTT is suitable for microstructure simulation. Most importantly, the FTT method can increase the spatial and temporal resolutions beyond the limits imposed by the available hardware compared with the conventional uniform mesh. At the simulation time of 0.03 s in this study, the computer memory used for computation is no more than 10 MB with the FTT method, while it is about 50 MB with the uniform mesh method. In addition, the proposed FTT method is more effi cient in computation time when compared with the uniform mesh method. It would take about 20 h for the uniform mesh method, while only 2 h for the FTT method for computation when the solidifi cation time is 0.17 s in this study.
基金supported by the National Natural Science Foundation of China(Nos.91752114 and 11672160)
文摘In the present paper, high-order finite volume schemes on unstructured grids developed in our previous papers are extended to solve three-dimensional inviscid and viscous flows. The highorder variational reconstruction technique in terms of compact stencil is improved to reduce local condition numbers. To further improve the efficiency of computation, the adaptive mesh refinement technique is implemented in the framework of high-order finite volume methods. Mesh refinement and coarsening criteria are chosen to be the indicators for certain flow structures. One important challenge of the adaptive mesh refinement technique on unstructured grids is the dynamic load balancing in parallel computation. To solve this problem, the open-source library p4 est based on the forest of octrees is adopted. Several two-and three-dimensional test cases are computed to verify the accuracy and robustness of the proposed numerical schemes.
文摘A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on α priori （sequentially） adapted meshes and study its convergence. The scheme on α priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find α priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in χ, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for improving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical solution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N^-1 = o （ε^v）, where N denotes the number of nodes in the spatial mesh, and the value v = v（K） can be chosen arbitrarily small for suitable K.
文摘A combined characteristic-based split algorithm and all adaptive meshing technique for analyzing two-dimensional viscous incompressible flow are presented. Tile method uses the three-node triangular element with equal-order interpolation functions for all variables of tile velocity components and pressure. The main advantage of the combined nlethod is that it inlproves the sohltion accuracy by coupling an error estinla- tion procedure to an adaptive meshing technique that generates small elements in regions with a large change ill sohmtion gradients, mid at the same time, larger elements in the other regions. The performance of the combined procedure is evaluated by analyzing one test case of the flow past a cylinder, for their transient and steady-state flow behaviors.
基金supported by the National Natural Science Foundation of China (11150110134)the Science Foundation of Aeronautics of China (20101271004)
文摘High-order schemes based on block-structured adaptive mesh refinement method are prepared to solve computational aeroacoustic （CAA） problems with an aim at improving computational efficiency. A number of numerical issues associated with high-order schemes on an adaptively refined mesh, such as stability and accuracy are addressed. Several CAA benchmark problems are used to demonstrate the feasibility and efficiency of the approach.
基金Sponsored by the National Natural Science Foundation of China(10676120)Laboratory of Computational Physics Foundation(9140C690101070C69)
文摘The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a conservative spatial interpolation, the time integration methodology with the adapitve time increment and an adaptive computational region method. The advantage of AMR technique is exhibited by numerical examples, including the 1-D C-J detonation and the 2-D implosion ignited from a single point. Results show that AMR can promote the computational efficiency, keeping the accuracy in interesting regions.
文摘The adaptive mesh mesh technique is developed and applied in three dimensional numerical simulation of welding process on the base of the commercial software. Special user subroutine is worked out to accom- plish this function.This technique can make the dense mesh moving simultaneously with the heat source while the other area of the structure with much coarser mesh, greatly reducing the number of nodes and elements in the analysis.Temperature field,displacement and stress distributions during welding pro- cess me analyzed by FEM method with adaptive mesh and the analysis is also conducted with normal FEM method. The temperature field,displacement and stress distributions obtained with both methods are shown in contrast. The results show that the temperature fields and the displacement distributions of simulation on adaptive mesh correspond wery well with that of without adaptive mesh. Though the stress distributions have some difference,but the trends of the stress distribution are corresponding.The com- parison of the computing time of the two meshes indicates that the adaptive that the adaptive mesh can greatly reduce the calculation time when used for welding process.
基金This project is supported by Provincial Project Foundation of Science and Technology of Guangdong, China(No.2002104040101).
文摘In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.
基金This work was supported by the National Natural Science Foun-dation of China(No.41776194).
文摘The present study provides a three-dimensional volume-of-fluid method based on the adaptive mesh refinement technique.The projection method on the adaptive mesh is introduced for solving the incompressible Navier-Stokes equations.The octree structure mesh is employed to solve the flow velocities and the pressure.The developed solver is applied to simulate the deformation of the cubic droplet driven by the surface tension without the effect of the gravity.The numerical results well predict the shape evolution of the droplet.
基金Supported by the National Natural Science Foundation of China(No.51379143 and No.51109018)the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(No.51021004)+1 种基金the Open Foundation of Key Laboratory of Water-Sediment Science and Water Disaster Prevention of Hunan Province(No.2014SS01)the Open Foundation of State Key Laboratory of Hydraulic Engineering Simulation and Safety(No.HSSKLTJU-201208)
文摘The technique of adaptive tree mesh is an effective way to reduce computational cost through automatic adjustment of cell size according to necessity. In the present study, the 2D numerical N-S solver based on the adaptive quadtree mesh system was extended to a 3D one, in which a spatially adaptive oetree mesh system and multiple particle level set method were adopted for the convenience to deal with the air-water-structure multiple-medium coexisting domain. The stretching process of a dumbbell was simulated and the results indicate that the meshes are well adaptable to the free surface. The collapsing process of water column impinging a circle cylinder was simulated and from the results, it can be seen that the processes of fluid splitting and merging are properly simulated. The interaction of second-order Stokes waves with a square cylinder was simulated and the obtained drag force is consistent with the result by the Morison＇s wave force formula with the coefficient values of the stable drag component and the inertial force component bein~ set as 2.54.
