A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Advection-Diffusion Problems

Peng, Piaopiao; Fu, Yida; Cheng, Yumin

doi:10.1142/s175882512150085x

Cited by 22 publications

(5 citation statements)

References 48 publications

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“…When large deformations occur, it is challenging to maintain the nonsingularity and continuity of the mesh. Accordingly, a series of mesh-less simulation methods such as smoothed particle hydrodynamics(SPH) [103][104][105][106], cracking particle model (CPM) [107,108], and reproducing kernel particle method (RKPM) [109,110] are proposed. Due to the separation of constraints from meshes and elements, meshless methods are particularly suitable for studying oversized deformation and crack growth such as impact.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

Dynamic characteristics and crack evolution laws of coal and rock under split Hopkinson pressure bar impact loading

Sun

Jin

et al. 2023

Meas. Sci. Technol.

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The aims of this paper are to comprehensively explore both the dynamic mechanical properties and crack evolution characteristics of coal and rock during impact failure. First, experimental specimens are prepared from coal seam, direct roof rock strata and direct floor rock strata in the same area to highlight the correlations between test pieces. Second, a dynamic strain gauge and high-speed (HS) camera are adopted to reflect the stress wave signal and crack evolution. Then, based on digital image correlation (DIC) technology and the mass screening method, the evolution laws of surface cracks during crushing and the distribution characteristics of sample fragments after crushing are studied from the perspective of fractal, and finally compared with those of the simulation analysis. The results are as follows. (1) The coal and rock samples from the same area have both consistency and differences. The dynamic mechanical properties of coal and rock are affected by the impact velocity and the physical properties of the specimen. Higher impact speeds and densities lead to the more obvious brittleness of the specimen when destroyed. Conversely, the sample shows more plasticity and ductile yield. (2) The self-similarity is significantly manifested in the evolution of surface cracks during impact and the distribution characteristics of fragments after impact. The box dimension and quality screening dimension are applicable to quantitatively characterize the evolution process and results of coal and rock fractures. (3) The simulation results based on the Holmquist–Johnson–Cook (HJC) and Riedel–Hiermaier–Thoma (RHT) constitutive models agree well with the experimental results, and the RHT constitutive model is more consistent. This study may contribute to a more comprehensive understanding of the dynamic characteristics and crack evolution laws of coal and rock under impact loading and provide references for further research and discussion.

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Section: Simulation Results and Discussionmentioning

confidence: 99%

Dynamic characteristics and crack evolution laws of coal and rock under split Hopkinson pressure bar impact loading

Sun

Jin

et al. 2023

Meas. Sci. Technol.

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“…In view of the advantage that the construction of the approximation function is only related to the discrete point and not related to the grid, the meshless method has received a lot of attention from many scholars in recent years [1][2][3][4]. Meshless methods have been widely used in scientific and engineering problems and have shown high accuracy and effectiveness [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

Wang¹,

Wu²,

Xu³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems. The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems. The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes. For extremely small singular diffusion coefficients, the numerical solution will avoid numerical oscillation and has high computational stability. KEYWORDSDimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method; interpolating variational multiscale element-free Galerkin (VMIEFG) method; dimension splitting method; singularly perturbed convection-diffusion problems

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“…By combining the traditional finite difference method with various kinds of meshless methods, thus the hybrid EFG method [26][27][28][29], the dimensional splitting complex variable EFG method [30][31][32][33][34], the dimension split reproducing kernel particle method [35][36][37][38] and the hybrid generalized interpolated EFG method [39] are proposed respectively, these methods can solve the multi-dimensional problems efficiently.…”

Section: Introductionmentioning

confidence: 99%

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

Cheng¹,

Xing²,

Peng³

2022

Computer Modeling in Engineering &Amp; Sciences

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In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steadystate heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form. The influences of node distribution, weight functions, scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively, and these numerical solutions show that less computational resources are spent when using the IEFG method.

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A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Advection-Diffusion Problems

Cited by 22 publications

References 48 publications

Dynamic characteristics and crack evolution laws of coal and rock under split Hopkinson pressure bar impact loading

Dynamic characteristics and crack evolution laws of coal and rock under split Hopkinson pressure bar impact loading

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

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