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三维瞬态对流扩散问题的插值型维数分裂无单元Galerkin方法

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提出一种求解三维瞬态对流扩散问题的插值型维数分裂无单元Galerkin(IDSEFG)方法.首先采用维数分裂法将该三维问题的空间域离散化处理得到一系列二维问题,使用插值型无单元Galerkin方法建立这些二维问题的离散系统方程,然后在维数分裂方向上利用有限差分法耦合这组离散方程,同时利用有限差分法离散时间域,最终得到此问题的IDSEFG方法计算公式.结合2个算例,讨论不同参数影响下的计算精度和效率.结果表明:IDSEFG方法在计算精度和速度上比改进的无单元Galerkin(IEFG)方法具有较大优势.
Interpolating dimension splitting element-free Galerkin method for 3D transient convection diffusion problems
An interpolating dimension splitting element-free Galerkin(IDSEFG)method for three-dimensional transient convection diffusion problem is presented.Firstly,the dimension splitting method is used to discretize the spatial domain of the three-dimensional problem into a series of two-dimensional problems.The interpolating element-free Galerkin method is employed to construct the discrete system equations for thesetwo-dimensional problems.Then,these equations are coupled via the finite difference method along the dimension splitting direction,while the time domain is also discretized using the finitedifference method.Finally,the computational formulas of the IDSEFG method are obtained.Two examples are given to discussthe computational accuracy and efficiency under differentparameter effects.The results show that the IDSEFG method has significant advantages over the improved element-free Galerkin(IEFG)method in terms of computational precision and speed.

meshless methodimproved interpolating moving least-squares methoddimension splittinginterpolating dimension splitting element-free Galerkin methodimproved element-free Galerkin methodtransient convection diffusion

成毓俊、彭妙娟、程玉民

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上海大学力学与工程科学学院,上海 200444

无网格方法 改进的移动最小二乘插值法 维数分裂 插值型维数分裂无单元Galerkin方法 改进的无单元Galerkin方法 瞬态对流扩散

2024

10.13340/j.cae.2024.04.010

计算机辅助工程
上海海事大学

计算机辅助工程

影响因子：0.388
ISSN：1006-0871
年,卷(期)：2024.33(4)