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A Comparative Study of State-of-the-Art Meshless Methods for Flow and Transport Simulation in Porous Media 认领 引用
1
作者 T.I.Eldho Sanjukta Das +1 位作者 Aatish Anshuman Tinesh Pathania 《Computer Modeling in Engineering & Sciences》 SCIE EI 2026年第5期828-852,共25页
In recent years,meshless methods have been increasingly applied to the simulation of various engineering problems due to their inherent advantages over traditional mesh-based approaches,including greater flexibility,i... In recent years,meshless methods have been increasingly applied to the simulation of various engineering problems due to their inherent advantages over traditional mesh-based approaches,including greater flexibility,independence from predefined meshing,simpler adaptive analysis,improved automation,and suitability for complex problems.Several meshless methods have been used for porous media simulation,and are broadly categorized into collocation,global weak form and local weak form methods.In this study,a comprehensive comparison of the applicability of these three categories of meshless methods for simulating coupled flow and transport problems in porous media is presented.The Radial Point Collocation Method(RPCM)(strong form),the Element Free Galerkin Method(EFGM)(global weak form)and the Meshless Local Petrov Galerkin(MLPG)method(local weak form)are implemented and systematically compared.These methods are applied to the analysis of flow in a synthetic regular domain aquifer,flow and non-reactive contaminant transport in a synthetic irregular boundary porous media problem and groundwater flow in a field aquifer located in India.The simulated groundwater heads are compared with analytical solution,observed field data and results obtained from widely used MODFLOW-MT3DMS models.The deviation of the solutions from the analytical solution is in the range of O.67%to O.l6%for the hypothetical case study.For the field-scale case study,mean absolute error of 0.183%,0.18l%and 0.188%are obtained for the RPCM,EFGM and MLPG models,respectively,outperforming MODFLOW,which exhibits a deviation of 0.254%from observed values.Overall,the present study reaffirms the practical applicability of these meshless methods for real-world groundwater problems and provides valuable insights into the utilization of each category of meshless method,with respect to problem type,computational efficiency and accuracy requirements. 展开更多
关键词 Meshless methods groundwater flow contaminant transport radial point collocation method element free Galerkin method meshless local Petrov Galerkin method
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The Space-Time Semi-Analytical Meshless Methods for Coupled Burgers'Equations 认领 引用
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作者 ZHANG Zhiqiang WANG Fuzhang 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第6期572-578,共7页
In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are c... In this paper,a simple direct space-time semi-analytical meshless scheme is proposed for the numerical approximation of the coupled Burgers'equations.During the whole solution procedure,two different schemes are considered in terms of radial and non-radial basis functions.The time-dependent variable in the first radial scheme is directly considered as the normal space variables to formulate an"isotropic"space-time radial basis function.The second non-radial scheme considered relationship between time-dependent and spacedependent variables.Under such circumstance,we can get a one-step space-time meshless scheme.The numerical findings demonstrate that the proposed meshless schemes are precise,user-friendly,and effective in solving the coupled Burgers'equations. 展开更多
关键词 radial basis functions coupled Burgers'equations meshless methods numerical simulation
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HIGH PERFORMANCE SPARSE SOLVER FOR UNSYMMETRICAL LINEAR EQUATIONS WITH OUT-OF-CORE STRATEGIES AND ITS APPLICATION ON MESHLESS METHODS 认领 引用 被引量：1
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作者 苑维然 陈璞 刘凯欣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第10期1339-1348,共10页
A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method ... A new direct method for solving unsymmetrical sparse linear systems（USLS） arising from meshless methods was introduced. Computation of certain meshless methods such as meshless local Petrov-Galerkin （MLPG） method need to solve large USLS. The proposed solution method for unsymmetrical case performs factorization processes symmetrically on the upper and lower triangular portion of matrix, which differs from previous work based on general unsymmetrical process, and attains higher performance. It is shown that the solution algorithm for USLS can be simply derived from the existing approaches for the symmetrical case. The new matrix factorization algorithm in our method can be implemented easily by modifying a standard JKI symmetrical matrix factorization code. Multi-blocked out-of-core strategies were also developed to expand the solution scale. The approach convincingly increases the speed of the solution process, which is demonstrated with the numerical tests. 展开更多
关键词 sparse matrices linear equations meshless methods high performance computation
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Quadric SFDI for Laplacian Discretisation in Lagrangian Meshless Methods 认领 引用 被引量：1
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作者 Shiqiang Yan Q.W.Ma Jinghua Wang 《Journal of Marine Science and Application》 CSCD 2020年第3期362-380,共19页
In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),... In the Lagrangian meshless(particle)methods,such as the smoothed particle hydrodynamics(SPH),moving particle semi-implicit(MPS)method and meshless local Petrov-Galerkin method based on Rankine source solution(MLPG_R),the Laplacian discretisation is often required in order to solve the governing equations and/or estimate physical quantities(such as the viscous stresses).In some meshless applications,the Laplacians are also needed as stabilisation operators to enhance the pressure calculation.The particles in the Lagrangian methods move following the material velocity,yielding a disordered(random)particle distribution even though they may be distributed uniformly in the initial state.Different schemes have been developed for a direct estimation of second derivatives using finite difference,kernel integrations and weighted/moving least square method.Some of the schemes suffer from a poor convergent rate.Some have a better convergent rate but require inversions of high order matrices,yielding high computational costs.This paper presents a quadric semi-analytical finite-difference interpolation(QSFDI)scheme,which can achieve the same degree of the convergent rate as the best schemes available to date but requires the inversion of significant lower-order matrices,i.e.3×3 for 3D cases,compared with 6×6 or 10×10 in the schemes with the best convergent rate.Systematic patch tests have been carried out for either estimating the Laplacian of given functions or solving Poisson’s equations.The convergence,accuracy and robustness of the present schemes are compared with the existing schemes.It will show that the present scheme requires considerably less computational time to achieve the same accuracy as the best schemes available in literatures,particularly for estimating the Laplacian of given functions. 展开更多
关键词 Laplacian discretisation Lagrangian meshless methods QSFDI Random/disordered particle distribution Poisson’s equation Patch tests
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The Space-Time Meshless Methods for the Solution of One-Dimensional Klein-Gordon Equations 认领 引用 被引量：2
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作者 ZHANG Zhiqiang WANG Fuzhang ZHANG Juan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2022年第4期313-320,共8页
A simple direct space-time meshless scheme,based on the radial or non-radial basis function,is proposed for the onedimensional Klein-Gordon equations.Since these equations are time-dependent,it is worthwhile to presen... A simple direct space-time meshless scheme,based on the radial or non-radial basis function,is proposed for the onedimensional Klein-Gordon equations.Since these equations are time-dependent,it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects.The first scheme is fulfilled by considering time variable as normal space variable,to construct an"isotropic"space-time radial basis function.The other scheme considered a realistic relationship between space variable and time variable which is not radial.The timedependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way.Numerical results show that the proposed meshless schemes are simple,accurate,stable,easy-to-program and efficient for the Klein-Gordon equations. 展开更多
关键词 radial basis functions meshless method space-time
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GALERKIN MESHLESS METHODS BASED ON PARTITION OF UNITY QUADRATURE 认领 引用 被引量：3
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作者 曾清红 卢德唐 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第7期893-899,共7页
Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature （PUQ）,for Galerkin meshless methods was presented. The technique is b... Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature （PUQ）,for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are “truly” meshless methods. 展开更多
关键词 Galerkin meshless method finite cover partition of unity numerical quadrature
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Three Boundary Meshless Methods for Heat Conduction Analysis in Nonlinear FGMs with Kirchhoff and Laplace Transformation 认领 引用 被引量：6
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作者 Zhuo-Jia Fu Wen Chen Qing-Hua Qin 《Advances in Applied Mathematics and Mechanics》 SCIE 2012年第5期519-542,共24页
This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of ... This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials(FGMs).The three methods are,respectively,the method of fundamental solution(MFS),the boundary knot method(BKM),and the collocation Trefftz method(CTM)in conjunction with Kirchhoff transformation and various variable transformations.In the analysis,Laplace transform technique is employed to handle the time variable in transient heat conduction problem and the Stehfest numerical Laplace inversion is applied to retrieve the corresponding time-dependent solutions.The proposed MFS,BKM and CTM are mathematically simple,easyto-programming,meshless,highly accurate and integration-free.Three numerical examples of steady state and transient heat conduction in nonlinear FGMs are considered,and the results are compared with those from meshless local boundary integral equation method(LBIEM)and analytical solutions to demonstrate the effi-ciency of the present schemes. 展开更多
关键词 Method of fundamental solution boundary knot method collocation Trefftz method Kirchhoff transformation Laplace transformation meshless method
Meshless methods for physics-based modeling and simulation of deformable models 认领 引用 被引量：2
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作者 GUO XiaoHu QIN Hong 《Science in China(Series F)》 2009年第3期401-417,共17页
As 3D digital photographic and scanning devices produce higher resolution images, acquired geometric data sets grow more complex in terms of the modeled objects＇ size, geometry, and topology. As a consequence, point-... As 3D digital photographic and scanning devices produce higher resolution images, acquired geometric data sets grow more complex in terms of the modeled objects＇ size, geometry, and topology. As a consequence, point-sampled geometry is becoming ubiquitous in graphics and geometric information processing, and poses new challenges which have not been fully resolved by the state-of-art graphical techniques. In this paper, we address the challenges by proposing a meshless computational framework for dynamic modeling and simulation of solids and thin-shells represented as point sam- ples. Our meshless framework can directly compute the elastic deformation and fracture propagation for any scanned point geometry, without the need of converting them to polygonal meshes or higher order spline representations. We address the necessary computational techniques, such as Moving Least Squares, Hierarchical Discretization, and Modal Warping, to effectively and efficiently compute the physical simulation in real-time. This meahless computational framework aims to bridge the gap between the point-sampled geometry with physics-based modeling and simulation governed by partial differential equations. 展开更多
关键词 meshless method physics-based modeling physics-based simulation deformable models
Advances in the Improved Element-Free Galerkin Methods:A Comprehensive Review 认领 引用 被引量：1
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作者 Heng Cheng YichenYang Yumin Cheng 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第12期2853-2894,共42页
The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieve... The element-free Galerkin(EFG)method,which constructs shape functions via moving least squares(MLS)approximation,represents a fundamental and widely studied meshless method in numerical computation.Although it achieves high computational accuracy,the shape functions are more complex than those in the conventional finite element method(FEM),resulting in great computational requirements.Therefore,improving the computational efficiency of the EFG method represents an important research direction.This paper systematically reviews significant contributions fromdomestic and international scholars in advancing the EFGmethod.Including the improved element-free Galerkin(IEFG)method,various interpolating EFG methods,four distinct complex variable EFG methods,and a series of dimension splitting meshless methods.In the numerical examples,the effectiveness and efficiency of the three methods are validated by analyzing the solutions of the IEFG method for 3D steadystate anisotropic heat conduction,3D elastoplasticity,and large deformation problems,as well as the performance of two-dimensional splitting meshless methods in solving the 3D Helmholtz equation. 展开更多
关键词 Meshless method improved element-free Galerkin method singular weight function nonsingular weight function interpolating element-free Galerkin method complex variable element-free Galerkin method dimension splitting method dimension splitting meshless method
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Numerical Simulation Method of Meshless Reservoir Considering Time-Varying Connectivity Parameters 认领 引用
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作者 Yuyang Liu Wensheng Zhou +4 位作者 Zhijie Wei Engao Tang Chenyang Shi Qirui Zhang Zifeng Chen 《Energy Engineering》 EI 2025年第10期4245-4260,共16页
After a long period of water flooding development,the oilfield has entered the middle and high water cut stage.The physical properties of reservoirs are changed by water erosion,which directly impacts reservoir develo... After a long period of water flooding development,the oilfield has entered the middle and high water cut stage.The physical properties of reservoirs are changed by water erosion,which directly impacts reservoir development.Conventional numerical reservoir simulation methodologies typically employ static assumptions for model construction,presuming invariant reservoir geological parameters throughout the development process while neglecting the reservoir’s temporal evolution characteristics.Although such simplifications reduce computational complexity,they introduce substantial descriptive inaccuracies.Therefore,this paper proposes a meshless numerical simulation method for reservoirs that considers time-varying characteristics.This method avoids the meshing in traditional numerical simulation methods.From the fluid flow perspective,the reservoir’s computational domain is discretized into a series of connection units.An influence domain with a certain radius centered on the nodes is selected,and one-dimensional connection units are established between the nodes to achieve the characterization of the flow topology structure of the reservoir.In order to reflect the dynamic evolution of the reservoir’s physical properties during the water injection development process,the time-varying characteristics are incorporated into the formula of the seepage characteristic parameters in the meshless calculation.The change relationship of the permeability under different surface fluxes is considered to update the calculated connection conductivity in real time.By combining with the seepage control equation for solution,a time-varying meshless numerical simulation method is formed.The results show that compared with the numerical simulationmethod of the connection elementmethod(CEM)that only considers static parameters,this method has higher simulation accuracy and can better simulate the real migration and distribution of oil and water in the reservoir.Thismethod improves the accuracy of reservoir numerical simulation and the development effect of oilfields,providing a scientific basis for optimizing the water injection strategy,adjusting the production plan,and extending the effective production cycle of the oilfield. 展开更多
关键词 Meshless method parameters’time-varying numerical simulation production optimization block application
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THEORETICAL ANALYSIS OF THE REPRODUCING KERNEL GRADIENT SMOOTHING INTEGRATION TECHNIQUE IN GALERKIN MESHLESS METHODS 认领 引用 被引量：1
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作者 Xiaolin Li 《Journal of Computational Mathematics》 SCIE CSCD 2023年第3期501-524,共24页
Numerical integration poses greater challenges in Galerkin meshless methods than finite element methods owing to the non-polynomial feature of meshless shape functions.The reproducing kernel gradient smoothing integra... Numerical integration poses greater challenges in Galerkin meshless methods than finite element methods owing to the non-polynomial feature of meshless shape functions.The reproducing kernel gradient smoothing integration(RKGSI)is one of the optimal numerical integration techniques in Galerkin meshless methods with minimum integration points.In this paper,properties,quadrature rules and the effect of the RKGSI on meshless methods are analyzed.The existence,uniqueness and error estimates of the solution of Galerkin meshless methods under numerical integration with the RKGSI are established.A procedure on how to choose quadrature rules to recover the optimal convergence rate is presented. 展开更多
关键词 Galerkin meshless method Numerical integration Quadrature rule Error estimates Element-free Galerkin method Degree of precision
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NUMERICAL ANALYSIS OF MINDLIN SHELL BY MESHLESS LOCAL PETROV-GALERKIN METHOD 认领 引用 被引量：5
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作者 Di Li Zhongqin Li Shuhui Li 《Acta Mechanica Solida Sinica》 SCIE EI 2008年第2期160-169,共10页
The objectives of this study are to employ the meshless local Petrov-Galerkin method （MLPGM） to solve three-dimensional shell problems. The computational accuracy of MLPGM for shell problems is affected by many fact... The objectives of this study are to employ the meshless local Petrov-Galerkin method （MLPGM） to solve three-dimensional shell problems. The computational accuracy of MLPGM for shell problems is affected by many factors, including the dimension of compact support domain, the dimension of quadrture domain, the number of integral cells and the number of Gauss points. These factors＇ sensitivity analysis is to adopt the Taguchi experimental design technology and point out the dimension of the quadrature domain with the largest influence on the computational accuracy of the present MLPGM for shells and give out the optimum combination of these factors. A few examples are given to verify the reliability and good convergence of MLPGM for shell problems compared to the theoretical or the finite element results. 展开更多
关键词 meshless methods meshless local Petrov-Galerkin method moving least square shell
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h-ADAPTIVE ANALYSIS BASED ON MESHLESS LOCAL PETROV-G ALERKIN METHOD WITH B SPLINE WAVELET FOR PLATES AND SHELLS 认领 引用 被引量：1
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作者 Di Li Zhongqin Lin 《Acta Mechanica Solida Sinica》 SCIE EI 2009年第4期337-346,共10页
Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as t... Using the two-scale decomposition technique, the h-adaptive meshless local Petrov- Galerkin method for solving Mindlin plate and shell problems is presented. The scaling functions of B spline wavelet are employed as the basis of the moving least square method to construct the meshless interpolation function. Multi-resolution analysis is used to decompose the field variables into high and low scales and the high scale component can commonly represent the gradient of the solution according to inherent characteristics of wavelets. The high scale component in the present method can directly detect high gradient regions of the field variables. The developed adaptive refinement scheme has been applied to simulate actual examples, and the effectiveness of the present adaptive refinement scheme has been verified. 展开更多
关键词 meshless methods meshless local Petrov-Galerkin method multi-resolution analysis adaptive analysis plate and shell
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Analysis of antisym metric cross-ply laminates using high-order shear deformation theories:a meshless approach 认领 引用 被引量：1
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作者 D.E.S.Rodrigues J.Belinha +1 位作者 L.M.J.S.Dinis R.M.Natal Jorge 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2020年第5期1078-1098,I0003,共21页
For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of severa... For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of several meshless methods,which are more flexible and equally accurate numerical methods.The meshless method used in this work is the natural neighbour radial point interpolation method(NNRPIM).In order to discretize the problem domain,the NNRPIM only requires an unstructured nodal distribution.Then,using the Voronoi mathematical concept,it enforces the nodal connectivity and constructs the background integration mesh.The NNRPIM shape functions are constructed using the radial point interpolation technique.In this work,the displacement field of composite laminated plates is defined by high-order shear deformation theories.In the end,several antisymmetric cross-ply laminates were analysed and the NNRPIM solutions were compared with the literature.The obtained results show the efficiency and accuracy of the NNRPIM formulation. 展开更多
关键词 Antisymmetric cross-ply laminates High-order shear deformation theories Meshless methods Naturalneighbour radial point interpolation method(NNRPIM)
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Meshless simulation for skeleton driven elastic deformation 认领 引用 被引量：1
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作者 SONG Chao ZHANG Hong-xin +1 位作者 HUANG Jin BAO Hu-jun 《Journal of Zhejiang University-SCIENCE A》 EI CAS 2006年第9期1596-1602,共7页
A meshless simulation system is presented for elastic deformation driven by skeleton in this paper. In this system, we propose a new method for calculating node rotation while applying a similar technique with stiffne... A meshless simulation system is presented for elastic deformation driven by skeleton in this paper. In this system, we propose a new method for calculating node rotation while applying a similar technique with stiffness warping to tackle the nonlinear large deformation. In our method, all node rotations are evaluated from sampling points in attached skeleton by con- structing and solving the diffusion partial differential equation. The experiments indicated that the method can enhance the sta- bility of the dynamics and avoid fussy sub-step calculation in static deformation edition. Moreover, rational deformation results for the area around the skeleton joints can be simulated without user interaction by adopting the simplified technique. 展开更多
关键词 Physically-based deformation Skeleton driven Meshless methods Rotation field
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A meshless moving morphable component-based method for structural topology optimization without weak material 认领 引用 被引量：6
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作者 Linyuan Li Chang Liu +2 位作者 Zongliang Du Weisheng Zhang Xu Guo 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第5期72-87,I0002,共16页
Traditional topology optimization methods often introduce weak artificial material to mimic voids to avoid the singularity of the global stiffness matrix and carry out topology optimization with a fixed finite element... Traditional topology optimization methods often introduce weak artificial material to mimic voids to avoid the singularity of the global stiffness matrix and carry out topology optimization with a fixed finite element(FE)mesh.This treatment,however,may not only increase the computational cost for structural analysis but also lead to unfavorable numerical instabilities,especially when large deformations and dynamic/buckling behaviors are involved.In the present work,a new meshless moving morphable component-based method(ML-MMC),which structural analysis is carried out only on the solid region occupied by components,is proposed.In this approach,the coupling of discrete components is achieved through the adaptively constructed influence domain of the meshless shape function.Therefore,the singularity problem of the stiffness matrix can be naturally avoided without introducing weak artificial material.Compared with traditional methods,the number of degrees of freedoms(DOFs)can be reduced substantially under this treatment.The effectiveness of the proposed approach is also illustrated by some representative examples. 展开更多
关键词 Topology optimization Moving morphable components(MMCs) Meshless method Influence domain Numerical integration
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A meshless method for the nonlinear generalized regularized long wave equation 认领 引用 被引量：13
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作者 王聚丰 白福浓 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第3期35-42,共8页
This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtain... This paper presents a meshless method for the nonlinear generalized regularized long wave （GRLW） equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method. A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm. Compared with numerical methods based on mesh, the meshless method for the GRLW equation only requires the.scattered nodes instead of meshing the domain of the problem. Some examples, such as the propagation of single soliton and the interaction of two solitary waves, are given to show the effectiveness of the meshless method. 展开更多
关键词 generalized regularized long wave equation meshless method moving least-squares approximation convergence
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A meshless method for the compound KdV-Burgers equation 认领 引用 被引量：23
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作者 程荣军 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第7期41-46,共6页
The element-free Galerkin （EFG） method for numerically solving the compound Korteweg-de Vries-Burgers （KdVB） equation is discussed in this paper. The Galerkin weak form is used to obtain the discrete equation and ... The element-free Galerkin （EFG） method for numerically solving the compound Korteweg-de Vries-Burgers （KdVB） equation is discussed in this paper. The Galerkin weak form is used to obtain the discrete equation and the essential boundary conditions are enforced by the penalty method. The effectiveness of the EFG method of solving the compound Korteweg-de Vries-Burgers （KdVB） equation is illustrated by three numerical examples. 展开更多
关键词 element-free Galerkin （EFG） method meshless method compound Korteweg-de Vries-Burgers （KdVB） equation solitary wave
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A new complex variable meshless method for transient heat conduction problems 认领 引用 被引量：11
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作者 王健菲 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第12期42-50,共9页
In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is pres... In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper. 展开更多
关键词 meshless method improved complex variable moving least-square approximation com-plex variable meshless method transient heat conduction problem
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New complex variable meshless method for advection-diffusion problems 认领 引用 被引量：11
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作者 王健菲 程玉民 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第3期92-98,共7页
In this paper,an improved complex variable meshless method（ICVMM） for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square（ICVMLS） approximation.The equi... In this paper,an improved complex variable meshless method（ICVMM） for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square（ICVMLS） approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency. 展开更多
关键词 meshless method improved complex variable moving least-square approximation improved complex variable meshless method advection-diffusion problem
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