The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

Cheng, Heng; Peng, Miaojuan

doi:10.3390/math10010014

Cited by 10 publications

(3 citation statements)

References 67 publications

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“…It is found that the motion trajectory of the internal store will change at different time under the same launch conditions, which is caused by the unsteady flow field of the internal bay. Some scholars [7][8][9][10][11][12] have studied the hybrid complex variable element-free Galerkin (HCVEFG) method, which can improve computational efficiency. The research of Westmoreland [13] showed that applying appropriate ejection force to the store is conducive to the separation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation about the Characteristics of the Store Released from the Internal Bay in Supersonic Flow

Cheng¹,

Si²,

Li³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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To understand the influence of the initial release conditions on the separation characteristics of the store and improve it under high Mach number (Ma = 4) flight conditions, the overset grid method and the Realizable k − ε turbulence model coupled with an equation with six degrees of freedom are used to simulate the store released from the internal bay. The motion trajectory and the attitude angle of the store separation under the conditions of different centroid, velocity, height and control measures are given by the calculated result. Through analysis, the position of the centroid will affect the separation of the store, which needs to be considered in the design. Increasing the launching height is conducive to the separation of the store. If the store has an initial velocity, it can leave the internal bay more quickly and reduce the probability of collision with the wall. Cylindrical rod and slanted aft wall control measures can improve the attitude of the store and make the store fall more smoothly.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation about the Characteristics of the Store Released from the Internal Bay in Supersonic Flow

Cheng¹,

Si²,

Li³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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show abstract

“…The MLS approximate functions have been improved to accelerate computational speed, including the Improved Moving Least-Squares (IMLS) approximation [6], interpolating MLS approximation [7,8], and complex variable MLS approximation [9,10]. Using these methods to construct shape functions resulted in the presentation of the IEFG method [11][12][13][14], interpolating EFG method [15][16][17][18][19][20], and complex variable EFG method [10,21,22], respectively.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Three-Dimensional Laplace Equations Using the Dimension Coupling Method

Liu,

Zuo,

Cheng

et al. 2023

Mathematics

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Due to the low computational efficiency of the Improved Element-Free Galerkin (IEFG) method, efficiently solving three-dimensional (3D) Laplace problems using meshless methods has been a longstanding research direction. In this study, we propose the Dimension Coupling Method (DCM) as a promising alternative approach to address this challenge. Based on the Dimensional Splitting Method (DSM), the DCM divides the 3D problem domain into a coupling of multiple two-dimensional (2D) problems which are handled via the IEFG method. We use the Finite Element Method (FEM) in the third direction to combine the 2D discretized equations, which has advantages over the Finite Difference Method (FDM) used in traditional methods. Our numerical verification demonstrates the DCM’s convergence and enhancement of computational speed without losing computational accuracy compared to the IEFG method. Therefore, this proposed method significantly reduces computational time and costs when solving 3D Laplace equations with natural or mixed boundary conditions in a dimensional splitting direction, and expands the applicability of the dimension splitting EFG method.

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“…The improved element-free Galerkin (IEFG) method [1], which is based on the improved moving least-squares (IMLS) approximation [2], is an important meshless method. In the paper submitted to this Special Issue by Cheng et al [3], the IEFG method for solving three-dimensional (3D) Helmholtz equations is proposed. The IMLS approximation is used to form the trial function, the penalty method is used to enforce the essential boundary conditions and Galerkin weak form of 3D Helmholtz equations are used to obtain the final discretized equations.…”

mentioning

confidence: 99%

Preface to the Special Issue on “Numerical Computation, Data Analysis and Software in Mathematics and Engineering”

Cheng

2022

Mathematics

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The Improved Element-Free Galerkin Method for 3D Helmholtz Equations

Cited by 10 publications

References 67 publications

Numerical Simulation about the Characteristics of the Store Released from the Internal Bay in Supersonic Flow

Numerical Simulation about the Characteristics of the Store Released from the Internal Bay in Supersonic Flow

Analyzing Three-Dimensional Laplace Equations Using the Dimension Coupling Method

Preface to the Special Issue on “Numerical Computation, Data Analysis and Software in Mathematics and Engineering”

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