A complete mesh free adaptive algorithm （MFAA）, with solution adaptation and geometric adaptation, is developed to improve the resolution of flow features and to replace traditional global refinement techniques in s...A complete mesh free adaptive algorithm （MFAA）, with solution adaptation and geometric adaptation, is developed to improve the resolution of flow features and to replace traditional global refinement techniques in structured grids. Unnecessary redundant points and elements are avoided by using the mesh free local clouds refinement technology in shock influencing regions and regions near large curvature places on the boundary. Inviscid compressible flows over NACA0012 and RAE2822 airfoils are computed. Finally numerical results validate the accuracy of the above method.展开更多
A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian fra...A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner, so that without any element it could be considered as a completely mesh free method. The method was tested with a numerical example, and reliable solution was obtained with high accuracy and efficiency.展开更多
A meshless and matrix-free fluid dynamics solver(SOMA)is introduced that avoids the need for user generated and/or analyzed grids,volumes,and meshes.Incremental building of the approximation avoids creation and invers...A meshless and matrix-free fluid dynamics solver(SOMA)is introduced that avoids the need for user generated and/or analyzed grids,volumes,and meshes.Incremental building of the approximation avoids creation and inversion of possibly dense block diagonal matrices and significantly reduces user interaction.Validation results are presented from the application of SOMA to subsonic,compressible,and turbulent flow over an adiabatic flat plate.展开更多
A novel numerical method is explored and named as mesh-free poly-cell Galerkin method. An improved moving least-square （MLS） scheme is presented, which can avoid the matrix inversion in standard MLS and can be used ...A novel numerical method is explored and named as mesh-free poly-cell Galerkin method. An improved moving least-square （MLS） scheme is presented, which can avoid the matrix inversion in standard MLS and can be used to construct shape functions possessing delta Kronecher property. A new type of local support is introduced to ensure the alignment of integral domains with the cells of the back-ground mesh, which will reduce the difficult in integration. An intensive numerical study is conducted to test the accuracy of the present method. It is observed that solutions with good accuracy can be obtained with the present method.展开更多
Metal forming plays an important role in manufacturing industry and is widely applied in industries.The tradi- tional finite element method(FEM)numerical simulation is commonly used to predict metal forming process.Co...Metal forming plays an important role in manufacturing industry and is widely applied in industries.The tradi- tional finite element method(FEM)numerical simulation is commonly used to predict metal forming process.Conventional finite element analysis of metal forming processes often breaks down due to severe mesh distortion,therefore time-consuming remeshing is necessary.Meshfree methods have been developed since 1977 and can avoid this problem.This new generation of computational methods reduces time-consuming model generation and refinement effort,and its shape function has higher order connectivity than FEM’s.In this paper the velocity shape functions are developed from a reproducing kernel approximation that satisfies consistency conditions and is used to analyze metal tension rigid viscoplastic deforming and Magnesium Alloy(MB 15)sheet superplastic ten- sion forming.A meshfree method metal forming modeling program is set up,the partition of unity method is used to compute the integrations in weak form equations and penalty method is used to impose the essential boundary condition exactly.Metal forming examples,such as sheet metal superplastic tension forming and metal rigid viscoplastic tension forming,are analyzed to demon- strate the performance of mesh free method.展开更多
In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement...In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.展开更多
网格生成所需人力资源和工作时间在整个流场数值模拟周期中占比较高,是计算流体力学应用软件的瓶颈。大量文献提供了结构网格质量特性对差分格式计算结果有影响的算例,但是很少给出正交性和光滑性影响误差的机理分析。分析了MUSCL和WEN...网格生成所需人力资源和工作时间在整个流场数值模拟周期中占比较高,是计算流体力学应用软件的瓶颈。大量文献提供了结构网格质量特性对差分格式计算结果有影响的算例,但是很少给出正交性和光滑性影响误差的机理分析。分析了MUSCL和WENO差分格式在非均匀网格上产生的几何诱导误差,发现正交性和误差之间并无直接关联,有影响的几何参数是相邻网格的偏转角。理论推导证明,误差主要源自控制方程和差分格式,提高网格质量特性能够明显减小几何诱导误差,但是不能完全消除。近年来作者致力于改进算法,先后提出离散等价方程及其等价离散准则(discrete equivalence equation and its discrete rule,DEER)和非结构有限差分法。通过对自由流保持和线性流保持等算例的模拟,利用改进的算法在质量较差的网格上也能得到较好的计算结果。展开更多
文摘A complete mesh free adaptive algorithm （MFAA）, with solution adaptation and geometric adaptation, is developed to improve the resolution of flow features and to replace traditional global refinement techniques in structured grids. Unnecessary redundant points and elements are avoided by using the mesh free local clouds refinement technology in shock influencing regions and regions near large curvature places on the boundary. Inviscid compressible flows over NACA0012 and RAE2822 airfoils are computed. Finally numerical results validate the accuracy of the above method.
基金Project supported by the Nation-al Natural Science Foundation of China(No.10372055)the Shanghai Leading Academic Discipline Project(No.Y0103)
文摘A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner, so that without any element it could be considered as a completely mesh free method. The method was tested with a numerical example, and reliable solution was obtained with high accuracy and efficiency.
基金The authors wish to express their appreciation to the reviewers for their helpful suggestions which greatly improved the presentation of this paper。
文摘A meshless and matrix-free fluid dynamics solver(SOMA)is introduced that avoids the need for user generated and/or analyzed grids,volumes,and meshes.Incremental building of the approximation avoids creation and inversion of possibly dense block diagonal matrices and significantly reduces user interaction.Validation results are presented from the application of SOMA to subsonic,compressible,and turbulent flow over an adiabatic flat plate.
文摘A novel numerical method is explored and named as mesh-free poly-cell Galerkin method. An improved moving least-square （MLS） scheme is presented, which can avoid the matrix inversion in standard MLS and can be used to construct shape functions possessing delta Kronecher property. A new type of local support is introduced to ensure the alignment of integral domains with the cells of the back-ground mesh, which will reduce the difficult in integration. An intensive numerical study is conducted to test the accuracy of the present method. It is observed that solutions with good accuracy can be obtained with the present method.
文摘Metal forming plays an important role in manufacturing industry and is widely applied in industries.The tradi- tional finite element method(FEM)numerical simulation is commonly used to predict metal forming process.Conventional finite element analysis of metal forming processes often breaks down due to severe mesh distortion,therefore time-consuming remeshing is necessary.Meshfree methods have been developed since 1977 and can avoid this problem.This new generation of computational methods reduces time-consuming model generation and refinement effort,and its shape function has higher order connectivity than FEM’s.In this paper the velocity shape functions are developed from a reproducing kernel approximation that satisfies consistency conditions and is used to analyze metal tension rigid viscoplastic deforming and Magnesium Alloy(MB 15)sheet superplastic ten- sion forming.A meshfree method metal forming modeling program is set up,the partition of unity method is used to compute the integrations in weak form equations and penalty method is used to impose the essential boundary condition exactly.Metal forming examples,such as sheet metal superplastic tension forming and metal rigid viscoplastic tension forming,are analyzed to demon- strate the performance of mesh free method.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110007)
文摘In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.
文摘网格生成所需人力资源和工作时间在整个流场数值模拟周期中占比较高,是计算流体力学应用软件的瓶颈。大量文献提供了结构网格质量特性对差分格式计算结果有影响的算例,但是很少给出正交性和光滑性影响误差的机理分析。分析了MUSCL和WENO差分格式在非均匀网格上产生的几何诱导误差,发现正交性和误差之间并无直接关联,有影响的几何参数是相邻网格的偏转角。理论推导证明,误差主要源自控制方程和差分格式,提高网格质量特性能够明显减小几何诱导误差,但是不能完全消除。近年来作者致力于改进算法,先后提出离散等价方程及其等价离散准则(discrete equivalence equation and its discrete rule,DEER)和非结构有限差分法。通过对自由流保持和线性流保持等算例的模拟,利用改进的算法在质量较差的网格上也能得到较好的计算结果。
