Adaptive mesh refinement (AMR) is fairly practiced in the context of high-dimensional, mesh-based computational models. However, it is in its infancy in that of low-dimensional, generalized-coordinate-based computatio...Adaptive mesh refinement (AMR) is fairly practiced in the context of high-dimensional, mesh-based computational models. However, it is in its infancy in that of low-dimensional, generalized-coordinate-based computational models such as projection-based reduced-order models. This paper presents a complete framework for projection-based model order reduction (PMOR) of nonlinear problems in the presence of AMR that builds on elements from existing methods and augments them with critical new contributions. In particular, it proposes an analytical algorithm for computing a pseudo-meshless inner product between adapted solution snapshots for the purpose of clustering and PMOR. It exploits hyperreduction—specifically, the energy-conserving sampling and weighting hyperreduction method—to deliver for nonlinear and/or parametric problems the desired computational gains. Most importantly, the proposed framework for PMOR in the presence of AMR capitalizes on the concept of state-local reduced-order bases to make the most of the notion of a supermesh, while achieving computational tractability. Its features are illustrated with CFD applications grounded in AMR and its significance is demonstrated by the reported wall-clock speedup factors.展开更多
A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface i...A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.展开更多
The paper presents the utilization of the adaptive Delaunay triangulation in the finite element modeling of two dimensional crack propagation problems, including detailed description of the proposed procedure which co...The paper presents the utilization of the adaptive Delaunay triangulation in the finite element modeling of two dimensional crack propagation problems, including detailed description of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around crack tips and large elements in the other regions. The resulting stress intensity factors and simulated crack propagation behavior are used to evaluate the effectiveness of the procedure. Three sample problems of a center cracked plate, a single edge cracked plate and a compact tension specimen, are simulated and their results assessed.展开更多
In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the s...In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes:a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.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
An adaptive finite element method for high-speed flow-structure interaction is pre- sented.The cell-centered finite element method is combined with an adaptive meshing technique to solve the Navier-Stokes equations fo...An adaptive finite element method for high-speed flow-structure interaction is pre- sented.The cell-centered finite element method is combined with an adaptive meshing technique to solve the Navier-Stokes equations for high-speed compressible flow behavior.The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite element method.The finite element formulation and computational procedure are de- scribed.Interactions between the high-speed flow,structural heat transfer,and deformation are studied by two applications of Mach 10 flow over an inclined plate,and Mach 4 flow in a channel.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
Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind sch...Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.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
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
A self adaptive three-dimensional baroclinic model is designed. A horizontal temperature gradient is used to control the grid size, which can improve computational precision in the fronts without inordinately increasi...A self adaptive three-dimensional baroclinic model is designed. A horizontal temperature gradient is used to control the grid size, which can improve computational precision in the fronts without inordinately increasing computation in the whole area. A simulation of the development and disappearance of the front in the Huanghai Sea is conducted with this model. Simulations of temperature distribution throughout the year are also conducted. The comoutational result agrees well with the observation.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
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 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
An essentially conservative adaptive space time conservation element and solution element (CE/SE) method is pro- posed for the effective simulation of shock-induced instability with low computational cost. Its imple...An essentially conservative adaptive space time conservation element and solution element (CE/SE) method is pro- posed for the effective simulation of shock-induced instability with low computational cost. Its implementation is based on redefined conservation elements (CEs) and solution elements (SEs), optimized interpolations and a Courant number insensitive CE/SE scheme. This approach is used in two applications, the Woodward double Mach reflection and a two- component Richtmyer-Meshkov instability experiment. This scheme reveals the essential features of the investigated cases, captures small unstable structures, and yields a solution that is consistent with the results from experiments or other high order methods.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 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
We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by sol...We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.展开更多
An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several poi...An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.展开更多
A discontinuity-capturing scheme of finite element method(FEM)is proposed.The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unstea...A discontinuity-capturing scheme of finite element method(FEM)is proposed.The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows,which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number. In particular,a new testing variable,i.e.,the disturbed kinetic energy E,is suggested and used in the adaptive mesh computation,which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number.Based on several calculated examples,this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows.展开更多
基金support by the Air Force Office of Scientific Research under Grant No.FA9550-20-1-0358 and Grant No.FA9550-22-1-0004.
文摘Adaptive mesh refinement (AMR) is fairly practiced in the context of high-dimensional, mesh-based computational models. However, it is in its infancy in that of low-dimensional, generalized-coordinate-based computational models such as projection-based reduced-order models. This paper presents a complete framework for projection-based model order reduction (PMOR) of nonlinear problems in the presence of AMR that builds on elements from existing methods and augments them with critical new contributions. In particular, it proposes an analytical algorithm for computing a pseudo-meshless inner product between adapted solution snapshots for the purpose of clustering and PMOR. It exploits hyperreduction—specifically, the energy-conserving sampling and weighting hyperreduction method—to deliver for nonlinear and/or parametric problems the desired computational gains. Most importantly, the proposed framework for PMOR in the presence of AMR capitalizes on the concept of state-local reduced-order bases to make the most of the notion of a supermesh, while achieving computational tractability. Its features are illustrated with CFD applications grounded in AMR and its significance is demonstrated by the reported wall-clock speedup factors.
基金supported by the Open Project of Key Laboratory of Aerospace EDLA,CASC(No.EDL19092208)。
文摘A computational framework for parachute inflation is developed based on the immersed boundary/finite element approach within the open-source IBAMR library.The fluid motion is solved by Peskin's diffuse-interface immersed boundary(IB)method,which is attractive for simulating moving-boundary flows with large deformations.The adaptive mesh refinement technique is employed to reduce the computational cost while retain the desired resolution.The dynamic response of the parachute is solved with the finite element approach.The canopy and cables of the parachute system are modeled with the hyperelastic material.A tether force is introduced to impose rigidity constraints for the parachute system.The accuracy and reliability of the present framework is validated by simulating inflation of a constrained square plate.Application of the present framework on several canonical cases further demonstrates its versatility for simulation of parachute inflation.
文摘The paper presents the utilization of the adaptive Delaunay triangulation in the finite element modeling of two dimensional crack propagation problems, including detailed description of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around crack tips and large elements in the other regions. The resulting stress intensity factors and simulated crack propagation behavior are used to evaluate the effectiveness of the procedure. Three sample problems of a center cracked plate, a single edge cracked plate and a compact tension specimen, are simulated and their results assessed.
文摘In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes:a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.
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.
基金The project supported by the Thailand Research Fund(TRF)
文摘An adaptive finite element method for high-speed flow-structure interaction is pre- sented.The cell-centered finite element method is combined with an adaptive meshing technique to solve the Navier-Stokes equations for high-speed compressible flow behavior.The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite element method.The finite element formulation and computational procedure are de- scribed.Interactions between the high-speed flow,structural heat transfer,and deformation are studied by two applications of Mach 10 flow over an inclined plate,and Mach 4 flow in a channel.
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 Department of Science & Technology, Government of India under research grant SR/S4/MS:318/06.
文摘Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper,we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function.It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter.Numerical experiments illustrate in practice the result of convergence proved theoretically.
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.
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The National Science and Technology Support Program of China under contract No.2011BAC03B02the National Natural Science Foundation of China under contract No. 40976002
文摘A self adaptive three-dimensional baroclinic model is designed. A horizontal temperature gradient is used to control the grid size, which can improve computational precision in the fronts without inordinately increasing computation in the whole area. A simulation of the development and disappearance of the front in the Huanghai Sea is conducted with this model. Simulations of temperature distribution throughout the year are also conducted. The comoutational result agrees well with the observation.
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.
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Project supported by the National Natural Science Foundation of China (Grant Nos.10732010,10972010,and 11028206)the Opening Project of State Key Laboratory of Explosion Science and Technology,China (Grant No.KFJJ13-5M)
文摘An essentially conservative adaptive space time conservation element and solution element (CE/SE) method is pro- posed for the effective simulation of shock-induced instability with low computational cost. Its implementation is based on redefined conservation elements (CEs) and solution elements (SEs), optimized interpolations and a Courant number insensitive CE/SE scheme. This approach is used in two applications, the Woodward double Mach reflection and a two- component Richtmyer-Meshkov instability experiment. This scheme reveals the essential features of the investigated cases, captures small unstable structures, and yields a solution that is consistent with the results from experiments or other high order methods.
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.
基金The work of A.Kurganov was supported in part by the National Natural Science Foundation of China grant 11771201by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.
基金supported by The National Key Research and Development Program of China(Grants Nos.2017YFA0603901 and 2017YFC1501901)The National Natural Science Foundation of China(Grant No.41522504)。
文摘An adaptive 2 D nonhydrostatic dynamical core is proposed by using the multi-moment constrained finite-volume(MCV) scheme and the Berger-Oliger adaptive mesh refinement(AMR) algorithm. The MCV scheme takes several pointwise values within each computational cell as the predicted variables to build high-order schemes based on single-cell reconstruction. Two types of moments, such as the volume-integrated average(VIA) and point value(PV), are defined as constraint conditions to derive the updating formulations of the unknowns, and the constraint condition on VIA guarantees the rigorous conservation of the proposed model. In this study, the MCV scheme is implemented on a height-based, terrainfollowing grid with variable resolution to solve the nonhydrostatic governing equations of atmospheric dynamics. The AMR grid of Berger-Oliger consists of several groups of blocks with different resolutions, where the MCV model developed on a fixed structured mesh can be used directly. Numerical formulations are designed to implement the coarsefine interpolation and the flux correction for properly exchanging the solution information among different blocks. Widely used benchmark tests are carried out to evaluate the proposed model. The numerical experiments on uniform and AMR grids indicate that the adaptive model has promising potential for improving computational efficiency without losing accuracy.
基金The project supported by the National Natural Science Foundation of China (10125210),the Hundred-Talent Programme of the Chinese Academy of Sciences and the Innovation Project of the Chinese Academy of Sciences (KJCX-SW-L04,KJCX2-SW-L2)
文摘A discontinuity-capturing scheme of finite element method(FEM)is proposed.The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows,which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number. In particular,a new testing variable,i.e.,the disturbed kinetic energy E,is suggested and used in the adaptive mesh computation,which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number.Based on several calculated examples,this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows.