The phase field model can coherently address the relatively complex fracture phenomenon,such as crack nucleation,branching,deflection,etc.The model has been extensively implemented in the finite element package Abaqus...The phase field model can coherently address the relatively complex fracture phenomenon,such as crack nucleation,branching,deflection,etc.The model has been extensively implemented in the finite element package Abaqus to solve brittle fracture problems in recent studies.However,accurate numerical analysis typically requires fine meshes to model the evolving crack path effectively.A broad region must be discretized without prior knowledge of the crack path,further augmenting the computational expenses.In this proposed work,we present an automated framework utilizing a posteriori error-indicator(MISESERI)to demarcate and sufficiently refine the mesh along the anticipated crack path.This eliminates the need for manual mesh refinement based on previous experimental/computational results or heuristic judgment.The proposed Python-based framework integrates the preanalysis,sufficient mesh refinement,and subsequent phase-field model-based numerical analysis with user-defined subroutines in a single streamlined pass.The novelty of the proposed work lies in integrating Abaqus’s native error estimation and mesh refinement capability,tailored explicitly for phase-field simulations.The proposed methodology aims to reduce the computational resource requirement,thereby enhancing the efficiency of the phase-field simulations while preserving the solution accuracy,making the framework particularly advantageous for complex fracture problems where the computational/experimental results are limited or unavailable.Several benchmark numerical problems are solved to showcase the effectiveness and accuracy of the proposed approach.The numerical examples present the proposed approach’s efficacy in the case of a complex mixed-mode fracture problem.The results show significant reductions in computational resources compared to traditional phase-field methods,which is promising.展开更多
To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direc...To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.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
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
In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with ...In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with various reconstruction algorithms. The reconstruction algorithms usually employ the Newton-Raphson iteration scheme to visualize the resistivity distribution inside the object. Accuracy of the imaging process depends not only on the algorithm used, but also on the scheme of finite element discretization. In this paper an adaptive mesh refinement is used in a modified reconstruction algorithm for the regularized Err. The method has a major impact on efficient solution of the forward problem as well as on achieving improved image resolution. Computer simulations indicate that the Newton-Raphson reconstruction algorithm for Err using adaptive mesh refinement performs better than the classical Newton-Raphson algorithm in terms of reconstructed image resolution.展开更多
In this study,a numerical model for simulating two-phase flow is developed.The Cartesian grid with Adaptive Mesh Refinement(AMR)is adopted to reduce the computational cost.An explicit projection method is used for the...In this study,a numerical model for simulating two-phase flow is developed.The Cartesian grid with Adaptive Mesh Refinement(AMR)is adopted to reduce the computational cost.An explicit projection method is used for the time integration and the Finite Difference Method(FDM)is applied on a staggered grid for the discretization of spatial derivatives.The Volume of Fluid(VOF)method with Piecewise-Linear Interface Calculation(PLIC)is extended to the AMR grid to capture the gas-water interface accurately.A coarse-fine interface treatment method is developed to preserve the flux conservation at the interfaces.Several two-dimensional(2D)and three-dimensional(3D)benchmark cases are carried out for the validation of the model.2D and 3D shear flow tests are conducted to validate the extension of the VOF method to the AMR grid.A 2D linear sloshing case is considered in which the model is proved to have 2nd-order accuracy in space.The efficiency of applying the AMR grid is discussed with a nonlinear sloshing problem.Finally,2D solitary wave past stage and 2D/3D dam break are simulated to demonstrate that the model is able to simulate violent interface problems.展开更多
Subdivision is a widely used technique for mesh refinement.Classic methods rely on fixed manually defined weighting rules and struggle to generate a finer mesh with appropriate details,while advanced neural subdivisio...Subdivision is a widely used technique for mesh refinement.Classic methods rely on fixed manually defined weighting rules and struggle to generate a finer mesh with appropriate details,while advanced neural subdivision methods achieve data-driven nonlinear subdivision but lack robustness,suffering from limited subdivision levels and artifacts on novel shapes.To address these issues,this paper introduces a neural mesh refinement(NMR)method that uses the geometric structural priors learned from fine meshes to adaptively refine coarse meshes through subdivision,demonstrating robust generalization.Our key insight is that it is necessary to disentangle the network from non-structural information such as scale,rotation,and translation,enabling the network to focus on learning and applying the structural priors of local patches for adaptive refinement.For this purpose,we introduce an intrinsic structure descriptor and a locally adaptive neural filter.The intrinsic structure descriptor excludes the non-structural information to align local patches,thereby stabilizing the input feature space and enabling the network to robustly extract structural priors.The proposed neural filter,using a graph attention mechanism,extracts local structural features and adapts learned priors to local patches.Additionally,we observe that Charbonnier loss can alleviate over-smoothing compared to L2 loss.By combining these design choices,our method gains robust geometric learning and locally adaptive capabilities,enhancing generalization to various situations such as unseen shapes and arbitrary refinement levels.We evaluate our method on a diverse set of complex three-dimensional(3D)shapes,and experimental results show that it outperforms existing subdivision methods in terms of geometry quality.See https://zhuzhiwei99.github.io/NeuralMeshRefinement for the project page.展开更多
Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration,noise and erosion damage.Modelling such a unsteady and hi...Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration,noise and erosion damage.Modelling such a unsteady and highly turbulent flow remains a challenging issue.In this paper,cloud cavitating flow in a venturi is calculated using the detached eddy simulation(DES)model combined with the Merkle model.The adaptive mesh refinement(AMR)method is employed to speed up the calculation and investigate the mechanisms for vortex development in the venturi.The results indicate the velocity gradients and the generalized fluid element strongly influence the formation of vortices throughout a cavitation cycle.In addition,the cavitation-turbulence coupling is investigated on the local scale by comparing with high-fidelity experimental data and using profile stations.While the AMR calculation is able to predict well the time-averaged velocities and turbulence-related aspects near the throat,it displays discrepancies further downstream owing to a coarser grid refinement downstream and under-performs compared to a traditional grid simulation.Additionally,the AMR calculation is unable to reproduce the cavity width as observed in the experiments.Therefore,while AMR promises to speed the process significantly by refining the grid only in regions of interest,it is comparatively in line with a traditional calculation for cavitating flows.Thus this study intends to provide a reference to employing the AMR as a tool to speed up calculations and be able to simulate turbulence-cavitation interactions accurately.展开更多
Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a hig...Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a high-resolution mesh.The present work,within OpenFOAM,proposes an effective modeling framework using the large eddy simulation(LES)approach along with the volume of fluid(VOF)method to simulate the two-phase flow system and applies the Schnerr-Sauer model to calculate the mass-transfer rate between water and vapor.The adaptive mesh refinement(AMR)which is a powerful tool for allocating high-resolution grids only to the region of the greatest concern is adopted for improving the solution of interfacial structures.The effect of grid size is firstly investigated and the time-averaged quantities are verified against the experimental data,and then simulations of cavitating flows are successfully achieved to precisely characterize the features of cavitation with automatically and dynamically refining the mesh.As the refinement only takes place in the interfacial region,high-precision simulations can be achieved with limited computational resources,and the method shows promising prospects for modeling of the multi-scale,time-critical and computationally intensive cavitating flows.展开更多
One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.Hi...One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinement.展开更多
In applications such as parallel mesh refinement,it remains a challenging issue to ensure the refined surface respects the original Computer-Aided Design(CAD)model accurately.In this paper,an ultralight geometry proce...In applications such as parallel mesh refinement,it remains a challenging issue to ensure the refined surface respects the original Computer-Aided Design(CAD)model accurately.In this paper,an ultralight geometry processing library is developed to resolve this issue effectively and efficiently.Here,we say the kernel is ultralight because it has a very small set of data-structures and algorithms by comparison with industrial-level geometry kernels.Within the library,a simplified surface boundary representation(B-rep)and a radial edge structure are developed respectively to depict the geometry model and the surface mesh,plus hash tables that record the connections between the geometry model and the surface mesh.Based on these data structures,a set of efficient algorithms are developed,which initializes the connection tables,projects a point back to the original geometry,etc.With these data-structure and algorithmic infrastructures set up,the callings of eight well-designed Application Programming Interfaces(APIs)are powerful enough to enable the parallel mesh refinement algorithm outputs a mesh respecting the input CAD model accurately.Numerical experiments will be finally presented to evaluate the performance of the overall parallel mesh refinement algorithm and the algorithms in relation with the developed library.展开更多
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources.The interface is repre...An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources.The interface is represented by the zero level set of a Lipschitz functionϕ(x,y).Our adaptive mesh refinement is done within a small tube of|ϕ(x,y)|δwith finer Cartesian meshes.The discrete linear system of equations is solved by a multigrid solver.The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically,therefore,reduce the size of the linear system of the equations.Numerical examples presented show the efficiency of the grid refinement strategy.展开更多
Based on an error estimate in terms of element edge vectors on arbitrary unstructured simplex meshes,we propose a new edge-based anisotropic mesh refinement algorithm.As the mesh adaptation indicator,the error estimat...Based on an error estimate in terms of element edge vectors on arbitrary unstructured simplex meshes,we propose a new edge-based anisotropic mesh refinement algorithm.As the mesh adaptation indicator,the error estimate involves only the gradient of error rather than higher order derivatives.The preferred refinement edge is chosen to reduce the maximal term in the error estimate.The algorithm is implemented in both two-and three-dimensional cases,and applied to the singular function interpolation and the elliptic interface problem.The numerical results demonstrate that the convergence order obtained by using the proposed anisotropic mesh refinement algorithm can be higher than that given by the isotropic one.展开更多
Three-dimensional forward modeling magnetotellurics （MT） problems. We present a is a challenge for geometrically complex new edge-based finite-element algorithm using an unstructured mesh for accurately and efficien...Three-dimensional forward modeling magnetotellurics （MT） problems. We present a is a challenge for geometrically complex new edge-based finite-element algorithm using an unstructured mesh for accurately and efficiently simulating 3D MT responses. The electric field curl-curl equation in the frequency domain was used to deduce the H （curl） variation weak form of the MT forward problem, the Galerkin rule was used to derive a linear finite-element equation on the linear-edge tetrahedroid space, and, finally, a BI-CGSTAB solver was used to estimate the unknown electric fields. A local mesh refinement technique in the neighbor of the measuring MT stations was used to greatly improve the accuracies of the numerical solutions. Four synthetic models validated the powerful performance of our algorithms. We believe that our method will effectively contribute to processing more complex MT studies.展开更多
Based on the characteristics of 3D bulk forming process, the arbitrary Lagrangian-Eulerian (ALE) formulation-based FEM is studied, and a prediction-correction ALE-based FEM is proposed which integrates the advantages ...Based on the characteristics of 3D bulk forming process, the arbitrary Lagrangian-Eulerian (ALE) formulation-based FEM is studied, and a prediction-correction ALE-based FEM is proposed which integrates the advantages of precisely predicting the boundary configuration of the deformed material, and of efficiently avoiding hexahedron remeshing processes. The key idea of the prediction-correction ALE FEM is elaborated in detail. Accordingly, the strategy of mesh quality control, one of the key enabling techniques for the 3D bulk forming process numerical simulation by the prediction-correction ALE FEM is carefully investigated, and the algorithm for hexahedral element refinement is formulated based on the mesh distortion energy.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 cavitating flow around a Delft Twist-11 hydrofoil is simulated using the large eddy simulation approach.The volume-of-fluid method incorporated with the Schnerr-Sauer cavitation model is utilized to track the wate...The cavitating flow around a Delft Twist-11 hydrofoil is simulated using the large eddy simulation approach.The volume-of-fluid method incorporated with the Schnerr-Sauer cavitation model is utilized to track the water-vapor interface.Adaptive mesh refinement(AMR)is also applied to improve the simulation accuracy automatically.Two refinement levels are conducted to verify the dominance of AMR in predicting cavitating flows.Results show that cavitation features,including the U-type structure of shedding clouds,are consistent with experimental observations.Even a coarse mesh can precisely capture the phase field without increasing the total cell number significantly using mesh adaption.The predicted shedding frequency agrees fairly well with the experimental data under refinement level 2.This study illustrates that AMR is a promising approach to achieve accurate simulations for multiscale cavitating flows within limited computational costs.Finally,the force element method is currently adopted to investigate the lift and drag fluctuations during the evolution of cavitation structure.The mechanisms of lift and drag fluctuations due to cavitation and the interaction between vorticity forces and cavitation are explicitly revealed.展开更多
In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh contro...In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh control device allows for efficient a priori and a posteriori mesh refinements.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
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
文摘The phase field model can coherently address the relatively complex fracture phenomenon,such as crack nucleation,branching,deflection,etc.The model has been extensively implemented in the finite element package Abaqus to solve brittle fracture problems in recent studies.However,accurate numerical analysis typically requires fine meshes to model the evolving crack path effectively.A broad region must be discretized without prior knowledge of the crack path,further augmenting the computational expenses.In this proposed work,we present an automated framework utilizing a posteriori error-indicator(MISESERI)to demarcate and sufficiently refine the mesh along the anticipated crack path.This eliminates the need for manual mesh refinement based on previous experimental/computational results or heuristic judgment.The proposed Python-based framework integrates the preanalysis,sufficient mesh refinement,and subsequent phase-field model-based numerical analysis with user-defined subroutines in a single streamlined pass.The novelty of the proposed work lies in integrating Abaqus’s native error estimation and mesh refinement capability,tailored explicitly for phase-field simulations.The proposed methodology aims to reduce the computational resource requirement,thereby enhancing the efficiency of the phase-field simulations while preserving the solution accuracy,making the framework particularly advantageous for complex fracture problems where the computational/experimental results are limited or unavailable.Several benchmark numerical problems are solved to showcase the effectiveness and accuracy of the proposed approach.The numerical examples present the proposed approach’s efficacy in the case of a complex mixed-mode fracture problem.The results show significant reductions in computational resources compared to traditional phase-field methods,which is promising.
基金financially supported by the National Natural Science Foundation of China(No.41574127 and 41174104)the National Key Technology R&D Program for the 13th five-year plan(No.2016ZX05018006-006)
文摘To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.
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.
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 National Natural Science Foundation of China（Grant No. 60075009）
文摘In electrical impedance tomography （EIT）, distribution of the internal resistivity or conductivity of an unknown object is esti- mated using measured boundary voltage data induced by different current patterns with various reconstruction algorithms. The reconstruction algorithms usually employ the Newton-Raphson iteration scheme to visualize the resistivity distribution inside the object. Accuracy of the imaging process depends not only on the algorithm used, but also on the scheme of finite element discretization. In this paper an adaptive mesh refinement is used in a modified reconstruction algorithm for the regularized Err. The method has a major impact on efficient solution of the forward problem as well as on achieving improved image resolution. Computer simulations indicate that the Newton-Raphson reconstruction algorithm for Err using adaptive mesh refinement performs better than the classical Newton-Raphson algorithm in terms of reconstructed image resolution.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.51779049,51879058,52071098,51979053).
文摘In this study,a numerical model for simulating two-phase flow is developed.The Cartesian grid with Adaptive Mesh Refinement(AMR)is adopted to reduce the computational cost.An explicit projection method is used for the time integration and the Finite Difference Method(FDM)is applied on a staggered grid for the discretization of spatial derivatives.The Volume of Fluid(VOF)method with Piecewise-Linear Interface Calculation(PLIC)is extended to the AMR grid to capture the gas-water interface accurately.A coarse-fine interface treatment method is developed to preserve the flux conservation at the interfaces.Several two-dimensional(2D)and three-dimensional(3D)benchmark cases are carried out for the validation of the model.2D and 3D shear flow tests are conducted to validate the extension of the VOF method to the AMR grid.A 2D linear sloshing case is considered in which the model is proved to have 2nd-order accuracy in space.The efficiency of applying the AMR grid is discussed with a nonlinear sloshing problem.Finally,2D solitary wave past stage and 2D/3D dam break are simulated to demonstrate that the model is able to simulate violent interface problems.
基金Project supported by the National Natural Science Foundation of China(Nos.62071427 and U21B2004)。
文摘Subdivision is a widely used technique for mesh refinement.Classic methods rely on fixed manually defined weighting rules and struggle to generate a finer mesh with appropriate details,while advanced neural subdivision methods achieve data-driven nonlinear subdivision but lack robustness,suffering from limited subdivision levels and artifacts on novel shapes.To address these issues,this paper introduces a neural mesh refinement(NMR)method that uses the geometric structural priors learned from fine meshes to adaptively refine coarse meshes through subdivision,demonstrating robust generalization.Our key insight is that it is necessary to disentangle the network from non-structural information such as scale,rotation,and translation,enabling the network to focus on learning and applying the structural priors of local patches for adaptive refinement.For this purpose,we introduce an intrinsic structure descriptor and a locally adaptive neural filter.The intrinsic structure descriptor excludes the non-structural information to align local patches,thereby stabilizing the input feature space and enabling the network to robustly extract structural priors.The proposed neural filter,using a graph attention mechanism,extracts local structural features and adapts learned priors to local patches.Additionally,we observe that Charbonnier loss can alleviate over-smoothing compared to L2 loss.By combining these design choices,our method gains robust geometric learning and locally adaptive capabilities,enhancing generalization to various situations such as unseen shapes and arbitrary refinement levels.We evaluate our method on a diverse set of complex three-dimensional(3D)shapes,and experimental results show that it outperforms existing subdivision methods in terms of geometry quality.See https://zhuzhiwei99.github.io/NeuralMeshRefinement for the project page.
基金supported by the Office of Naval Research,USA(Grant No.N00014-18-S-B001)the Macao Young Scholars Program(Grant No.AM2022003)the Priority Postdoctoral Projects in Zhejiang Province(Grant No.341781).
文摘Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration,noise and erosion damage.Modelling such a unsteady and highly turbulent flow remains a challenging issue.In this paper,cloud cavitating flow in a venturi is calculated using the detached eddy simulation(DES)model combined with the Merkle model.The adaptive mesh refinement(AMR)method is employed to speed up the calculation and investigate the mechanisms for vortex development in the venturi.The results indicate the velocity gradients and the generalized fluid element strongly influence the formation of vortices throughout a cavitation cycle.In addition,the cavitation-turbulence coupling is investigated on the local scale by comparing with high-fidelity experimental data and using profile stations.While the AMR calculation is able to predict well the time-averaged velocities and turbulence-related aspects near the throat,it displays discrepancies further downstream owing to a coarser grid refinement downstream and under-performs compared to a traditional grid simulation.Additionally,the AMR calculation is unable to reproduce the cavity width as observed in the experiments.Therefore,while AMR promises to speed the process significantly by refining the grid only in regions of interest,it is comparatively in line with a traditional calculation for cavitating flows.Thus this study intends to provide a reference to employing the AMR as a tool to speed up calculations and be able to simulate turbulence-cavitation interactions accurately.
基金Project supported by the China Postdoctoral Science Foundation(Grant No.2018M630502)This work was supported by the Jiangsu Province Science Foundation for Youths(Grant No.BK20180505)the Fundamental Research Funds for the Central Universities(Grant No.2019B14914)。
文摘Cavitating flows are dominated by large gradients of physical properties and quantities containing complicated interfacial structures and lots of multi-scale eddies that need to be accurately characterized using a high-resolution mesh.The present work,within OpenFOAM,proposes an effective modeling framework using the large eddy simulation(LES)approach along with the volume of fluid(VOF)method to simulate the two-phase flow system and applies the Schnerr-Sauer model to calculate the mass-transfer rate between water and vapor.The adaptive mesh refinement(AMR)which is a powerful tool for allocating high-resolution grids only to the region of the greatest concern is adopted for improving the solution of interfacial structures.The effect of grid size is firstly investigated and the time-averaged quantities are verified against the experimental data,and then simulations of cavitating flows are successfully achieved to precisely characterize the features of cavitation with automatically and dynamically refining the mesh.As the refinement only takes place in the interfacial region,high-precision simulations can be achieved with limited computational resources,and the method shows promising prospects for modeling of the multi-scale,time-critical and computationally intensive cavitating flows.
文摘One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinement.
文摘In applications such as parallel mesh refinement,it remains a challenging issue to ensure the refined surface respects the original Computer-Aided Design(CAD)model accurately.In this paper,an ultralight geometry processing library is developed to resolve this issue effectively and efficiently.Here,we say the kernel is ultralight because it has a very small set of data-structures and algorithms by comparison with industrial-level geometry kernels.Within the library,a simplified surface boundary representation(B-rep)and a radial edge structure are developed respectively to depict the geometry model and the surface mesh,plus hash tables that record the connections between the geometry model and the surface mesh.Based on these data structures,a set of efficient algorithms are developed,which initializes the connection tables,projects a point back to the original geometry,etc.With these data-structure and algorithmic infrastructures set up,the callings of eight well-designed Application Programming Interfaces(APIs)are powerful enough to enable the parallel mesh refinement algorithm outputs a mesh respecting the input CAD model accurately.Numerical experiments will be finally presented to evaluate the performance of the overall parallel mesh refinement algorithm and the algorithms in relation with the developed library.
文摘An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources.The interface is represented by the zero level set of a Lipschitz functionϕ(x,y).Our adaptive mesh refinement is done within a small tube of|ϕ(x,y)|δwith finer Cartesian meshes.The discrete linear system of equations is solved by a multigrid solver.The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically,therefore,reduce the size of the linear system of the equations.Numerical examples presented show the efficiency of the grid refinement strategy.
基金supported by the National Basic Research Program under the Grant 2005CB321701the National Science Foundation of China under the grant 10771008 and 10771211partial supported by A Foundation for the Author of National Excellent Doctoral Dissertation of PRC.
文摘Based on an error estimate in terms of element edge vectors on arbitrary unstructured simplex meshes,we propose a new edge-based anisotropic mesh refinement algorithm.As the mesh adaptation indicator,the error estimate involves only the gradient of error rather than higher order derivatives.The preferred refinement edge is chosen to reduce the maximal term in the error estimate.The algorithm is implemented in both two-and three-dimensional cases,and applied to the singular function interpolation and the elliptic interface problem.The numerical results demonstrate that the convergence order obtained by using the proposed anisotropic mesh refinement algorithm can be higher than that given by the isotropic one.
基金National High Technology Research and Development Program(863 Program)(No.2006AA06Z105,2007AA06Z134)
文摘Three-dimensional forward modeling magnetotellurics （MT） problems. We present a is a challenge for geometrically complex new edge-based finite-element algorithm using an unstructured mesh for accurately and efficiently simulating 3D MT responses. The electric field curl-curl equation in the frequency domain was used to deduce the H （curl） variation weak form of the MT forward problem, the Galerkin rule was used to derive a linear finite-element equation on the linear-edge tetrahedroid space, and, finally, a BI-CGSTAB solver was used to estimate the unknown electric fields. A local mesh refinement technique in the neighbor of the measuring MT stations was used to greatly improve the accuracies of the numerical solutions. Four synthetic models validated the powerful performance of our algorithms. We believe that our method will effectively contribute to processing more complex MT studies.
基金the National Natural Science Foundation of China(No.50275094).
文摘Based on the characteristics of 3D bulk forming process, the arbitrary Lagrangian-Eulerian (ALE) formulation-based FEM is studied, and a prediction-correction ALE-based FEM is proposed which integrates the advantages of precisely predicting the boundary configuration of the deformed material, and of efficiently avoiding hexahedron remeshing processes. The key idea of the prediction-correction ALE FEM is elaborated in detail. Accordingly, the strategy of mesh quality control, one of the key enabling techniques for the 3D bulk forming process numerical simulation by the prediction-correction ALE FEM is carefully investigated, and the algorithm for hexahedral element refinement is formulated based on the mesh distortion energy.
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financially supported by the National Natural Science Foundation of China(Nos.U21A20126 and 52006197)the National Science Foundation of Zhejiang Province(Nos.LQ21E060012 and LR20E090001)the Key Research and Development Program of Zhejiang Province(No.2021C05006)。
文摘The cavitating flow around a Delft Twist-11 hydrofoil is simulated using the large eddy simulation approach.The volume-of-fluid method incorporated with the Schnerr-Sauer cavitation model is utilized to track the water-vapor interface.Adaptive mesh refinement(AMR)is also applied to improve the simulation accuracy automatically.Two refinement levels are conducted to verify the dominance of AMR in predicting cavitating flows.Results show that cavitation features,including the U-type structure of shedding clouds,are consistent with experimental observations.Even a coarse mesh can precisely capture the phase field without increasing the total cell number significantly using mesh adaption.The predicted shedding frequency agrees fairly well with the experimental data under refinement level 2.This study illustrates that AMR is a promising approach to achieve accurate simulations for multiscale cavitating flows within limited computational costs.Finally,the force element method is currently adopted to investigate the lift and drag fluctuations during the evolution of cavitation structure.The mechanisms of lift and drag fluctuations due to cavitation and the interaction between vorticity forces and cavitation are explicitly revealed.
文摘In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh control device allows for efficient a priori and a posteriori mesh refinements.
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.
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.
